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

3%10%

54%

14%

14%

5%

Transfer Costs of Land &Building

Real Estate Developers'Margin

Machinery & Equipment

Public Construction

Private Residential

Private: Non-residential

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

-.15

-.10

-.05

.00

.05

.10

.15

.20

1975 1980 1985 1990 1995 2000

GDP INVESTMENT

Business Cycle Volatility of Real Investmentin Hong Kong

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 can be measured in constant or current price terms.

Marginal productivity of capital is often thought to be roughly proportional to average productivity capital.

Value of OutputAPK

Value of Capital

K

MPK

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 to buy 1 capital good at interest rate 1+i.

The firm produces PMPKt+1 worth of goods and sells the capital good for .

Optimal to buy capital good as long as pay-off is greater than the cost.

Optimal Condition

Definition of Capital Cost

,K NEWtP

,K OLDtP

, , ,1[ ]

t

K NEW K OLD K NEWt t t

PMPK

iP P P

Cost of Capital

, ,1 1K OLD K NEW

t t t tP PMPK i P

Capital Cost

We can divide the capital cost into three parts.

1. Interest cost: Net interest rate.

2. Depreciation: Defined as change in value due to aging.

3. Capital gain: Defined as change in value due to change in price of new goods.

, , ,1

,

[ ]K

K NEW K OLD K NEWt t t

P K NEWt

ck iP P P

i g P

, ,1 1

,

K NEW K OLDt t

K NEWt

P P

P

, ,1

,

KK NEW K NEW

P t tK NEWt

P Pg

P

Real Capital Cost

We can convert the optimal capital equation into real terms by dividing both sides by the price level.

Define the real price of capital good as price of capital good relative to the firm’s output price.

,1

,1

,1

K

K

K

P K NEWt t

P K NEWt t

p K NEWt t t

PMPK i g P

MPK i g p

MPK r g p rck

,K NEWk tt

t

Pp

P

K

,K NEW

PMPK

P

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

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.

34$200,000 N

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.

Marginal MarginalTaxis Revenues Costs Profits Earnings Cost

1 200000 100000 100000 200000 1000002 336358.6 200000 136358.6 136358.6 1000003 455901.4 300000 155901.4 119542.8 1000004 565685.4 400000 165685.4 109784 1000005 668740.3 500000 168740.3 103054.9 1000006 766731.7 600000 166731.7 97991.42 1000007 860703.4 700000 160703.4 93971.69 1000008 951365.7 800000 151365.7 90662.28 1000009 1039230 900000 139230.5 87864.79 100000

10 1124683 1000000 124682.7 85452.17 100000

Optimal Capital: Example

Solve for Optimal Level of Capital

14

$150,000(.04 .08 .02) $1,000,000 KPMPK ck P

N

14 * * 4$150,000

1.5 5.0625$100,000

N N

K

ck

K*

,K NEW

PMPK

P

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.

K

ck

K* K**

,K NEW

PMPK

P

,

'K NEW

PMPK

P

K

ck

K*

ck’

K**

,K NEW

PMPK

P

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 2 3(1 ) (1 ) (1 ) (1 )

KP K NEWt tPMPK s i s s g P

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 property is rent, R.

Define rental yield, y, as the ratio of rent to property prices, PPE.

Capital cost of real estate includes Interest rate, i Depreciation/

Maintenance Costs δ

Property Taxes: τ Other Costs: c Capital Gains,

REPgRE

RE

PMPK R

Ry

P

( )

RERE P REck i c g P

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.

1 1

( )RE

RERE P

Ry ck P R R

P ck i c g

Ceteris Paribas

Curve PRE

R ↑ → ↑

i ↑ ← ↓

δ ↑ ← ↓

τ ↑ ← ↓

c ↑ ← ↓

↑ → ↑REPg

Real Estate Pricing

PRE

45%

1R

ck

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

Dec-1988 Dec-1990 Dec-1992 Dec-1994 Dec-1996 Dec-1998 Dec-2000 Dec-2002

7000

6500

6000

5500

5000

4500

4000

3500

3000

2500

2000

1500

HK: Property Capital Value: Residential: MediumHKD/Sq ft

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

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).

Market Value of Firm

Replacement Cost of Capitalq

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 they pay for the stock.

A firm generates a certain amount of profits per unit of capital

Profits

Market Capitalizationck

Profits

Price of CapitalMPK

ProfitsPrice of Capital

Profits

Market Capitalization

Market Capitalization

Price of Capital

MPKq

ck

Investment & the Stock Market

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? 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 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.