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
Why don’t people want to borrow at 2.5%
to make 5.1% returns?
Consider the theory of investment in real
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
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
Gross Investment refers to purchases of
Net Investment is Gross Investment
Components of Investment
Machinery & Equipment
Changes in Stocks – Inventory
Gross Fixed Capital Formation:
Transfer Costs of Land &
Real Estate Developers'
Machinery & Equipment
Investment expenditure is a
substantial share of GDP, but not as
large as consumption.
Fixed and inventory investment are
closely correlated with the business
Investment is an especially volatile
part of GDP.
Business Cycle Volatility
Business Cycle Volatility of Real Investment
in Hong Kong
1975 1980 1985 1990 1995 2000
Economists use marginal analysis to
determine an optimal level of an activity.
Most activities have diminishing marginal
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.
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
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.
Cost of Capital
Economists define the (time) cost of capital as the
cost of holding a unit of capital for a period of
A firm invests in capital equipment for a period.
The firm borrows money upfront to finance the
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
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
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
Optimal to buy capital iPt K , NEW [ Pt 1,OLD Pt K , NEW ]
good as long as pay-
off is greater than the Cost of Capital
We can divide the ck iPt K , NEW [ Pt 1,OLD Pt K , NEW ]
capital cost into three
i g PK
Pt K , NEW
1. Interest cost: Net
interest rate. Pt 1, NEW Pt 1,OLD
2. Depreciation: Defined Pt K , NEW
as change in value
due to aging.
3. Capital gain: Defined Pt 1, NEW Pt K , NEW
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
equation into real MPK i g tP 1 ptK , NEW
terms by dividing both
sides by the price MPK r gtp 1 ptK , NEW rckt
Define the real price
of capital good as Pt K , NEW
price of capital good pt
relative to the firm’s
P K , NEW
A taxi agency can produce a certain
amount of revenue with larger numbers
Assume earnings (revenues minus wages
minus costs) per year is given by the
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%
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
less than cost of 4
8 951365.7 800000 151365.7 90662.28 100000
Maximum profits 9 1039230 900000 139230.5 87864.79 100000
10 1124683 1000000 124682.7 85452.17 100000
Optimal Capital: Example
Solve for Optimal Level of Capital
PMPK 1 (.04 .08 .02) $1, 000, 000 ck P K
$150, 000 14 *
N N * 1.54 5.0625
P K , NEW
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
P K , NEW
P K , NEW
P K , NEW
The stock of capital may not be
particularly volatile over the business
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
Corporations frequently must pay taxes
on earnings. Define taxrate, .
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
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 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
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
Other Costs: c
PMPK RE R RE
Capital Gains, g
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
P ck (i c g )
R↑ → ↑
i↑ ← ↓
δ↑ ← ↓
τ↑ ← ↓
c↑ ← ↓
g P RE
↑ → ↑
Real Estate Pricing
A key determinant of the price of
real estate is the expected capital
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
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
Replacement Cost of Capital
The market value of a publicly listed firm without
debt is market capitalization (stock price * shares
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
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
If q = 1, firm should have zero net investment.
If q < 1, firm should have negative net
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
they pay for the stock. ck
A firm generates a certain amount of
profits per unit of capital MPK
Price of Capital
Price of Capital
Market Capitalization MPK
Price of Capital ck
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
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
Firms may be limited in
ability to raise funds in
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
Benchmark M-M Theory says investment
decisions and firm value should not
depend on sources of financing.
No distortionary taxation
Perfect financial markets with perfect
Internal Funds are cheaper form of
financing than external funds.
Much of corporate financing is through
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
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