International Financial Management
Chapter 5 International financial management
Michael Connolly
School of Business Administration,
University of Miami
Michael Connolly © 2007
Chapter 5
1
Summary
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Capital structure of the firm
The weighted average cost of borrowing
Cross-listing on foreign stock exchanges
Transfer pricing
International taxation
Working capital
Cash netting
Mergers and acquisitions
Offshore banking
An international business plan
Optimal international investing
Chapter 5
Page 2
Capital structure
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There are two ways of financing your
firm, by contracting debt (business loans)
or issuing equity (shares).
Creditors have senior debt that must be
paid or satisfied, except in the case of
bankruptcy. Shareholders participate in
ownership of the firm, so they share in
business risk and risk of bankruptcy.
Due to the greater risk, shareholders
typically require a higher rate of return
on their equity. Interest payments to
creditors are treated as an expense, so
they are a “tax shield” for the firm
Chapter 5
Page 3
Capital structure

The cost of capital is thus a weighted
average of the after-tax cost of
borrowing (D) and the cost of issuing
equity (E).
 D 
 E 
WACC  RD 1  t c 
  RE 

DE
DE
where WACC indicates the weighted
average cost of capital, R D the cost of
debt, D, R E the cost of equity, E, and
the marginal corporate tax rate.
Chapter 5
tc
Page 4
Capital structure
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For example, assume your firm has 30%
debt and 70% equity. It can borrow at
10% by selling its corporate bonds, while
its shareholders require a 14% return on
investment due to a 9.5% market risk
premium on your company.
Consequently, the weighted average cost
of capital is:
11.05%  10%1  0.350.3  14%0.7

Your firm should use this rate to discount
future cash flows.
Chapter 5
Page 5
Capital structure
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Due to the tax shield of borrowing and to
the low degree of risk to the initial loans,
the WACC initially declines with greater
financial leverage.
With a high degree of financial leverage
approaching one), the risk of financial
distress and bankruptcy increase.
This causes both the borrowing rate and
the equity rate to rise sharply.
Chapter 5
Page 6
Capital structure
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Consequently, there is an optimum capital
structure which minimizes the weighted
average cost of capital
Chapter 5
Page 7
International capital structure
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International capital structure - , the
basic rule for conversion of the WACC in
dollars to say pounds for purposes of
discounting pound cash flows, the interest
rate parity rule is:
or
 1  WACC£

 1  WACC
$

  1  RUK
  

  1  RUS



 1  RUK
WACC£  1  WACC$ 
 1  RUS
Chapter 5

  1

Page 8
International capital structure

If your weighted average cost of capital is
11.05% in USD, Treasuries in the U.K yield
3.0% and in the U.S. 4.5%, your WACC in
pounds is:
 1.03 
10.9%  1.1105
 1
 1.045 

reflecting the lower expected inflation rate
in the U.K.
When risk free Treasuries are not available,
the expected inflation rates may be
substituted for the interest rates: That is
use PPP instead of IRP.
Chapter 5
Page 9
Crosslisting on foreign stock exchanges
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Crosslisting on foreign stock exchanges By crosslisting its shares on foreign stock
exchanges - despite additional disclosure,
listing and reporting costs - a firm can
improve the liquidity of its existing shares
by making it easier for foreign shareholders
to acquire shares at home in their own
currencies.
Crosslisting may also increase the share
price by overcoming mis-pricing in a
segmented, illiquid, home capital market.
Chapter 5
Page 10
Transfer pricing

Transfer pricing refers to pricing of the
transfer of goods, services, and technology
between related units of the firm. It is
done both domestically and internationally.
The marginal cost of the
marketing and the production
divisions are summed
vertically to yield the
marginal cost of the final
product. Setting marginal
cost of the final product
equal to its marginal product
yields the profit-maximizing
level of production, 100, and
a price of $8.
Chapter 5
Page 11
Transfer pricing
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To provide the correct incentives to the
production division, a transfer price of $3
is optimal. In its production decisions, the
production division sets marginal cost equal
to $3 to maximize profits, producing
exactly the required amount of
intermediate inputs.
When there is a possibility to buy or sell
the intermediate input externally to other
firms at a fixed price, the firm should
regard this price as the opportunity cost of
the intermediate input.
Chapter 5
Page 12
Transfer pricing
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When the market for the intermediate
good is not competitive, the marketing
division should set a higher transfer price
to its internal division, and restrict its
purchases slightly from the external market.
Profit-maximization requires:
Pt
1
 1
Px
e
Where
Pt
represents the transfer price,
Px
the price at which the firm purchases the input on the
external market, and e the elasticity of supply of the
intermediate input to the marketing division.
Chapter 5
Page 13
Transfer pricing

Abusive transfer pricing takes place for the
main purpose of reducing taxation by
shifting profits from high tax to low tax
jurisdictions, if not to tax havens.
In this example, Stanly Wurks, CT
produces a hammer at a marginal
cost of $2, sells it for $1, a loss of
$1, to the FSC located in a
Bahamian tax haven. In turn,
Stanly Wurks, Europe pays $5 to
the FSC and sells the hammer at
$3.75 in Europe, losing $1.25.
The IRS could penalize this
abuse of transfer pricing.
Chapter 5
Page 14
Transfer pricing
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If the production division produces more of
the intermediate input than sold to the
marketing division and has monopoly power
in the market for the intermediate input,
its optimal transfer price is below the price
at which it sells the intermediate input to
the external market.
Pt
1
 1
Px
h
where h is the absolute value of the
elasticity of market demand for the
intermediate good.
Chapter 5
Page 15
Transfer pricing
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For example, if h = 2, the optimum
transfer price is 50% below the price at
which the intermediate input is sold on the
external market.
If the external market were perfectly
competitive, h approaches infinity, and the
optimal transfer price equals the market
price of the intermediate good.
Chapter 5
Page 16
International taxation
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The General Agreement on Tariffs and
Trade (GATT) of the World Trade
Organization (WTO) governs the tax
treatment of branches and subsidiaries
located abroad. If a branch or subsidiary
is located in a signatory country, it is
entitled to “national treatment” - that is,
tax and regulatory treatment no less
favorable than that accorded to national
enterprises.
Chapter 5
Page 17
International taxation
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Article III National Treatment on Internal
Taxation and Regulation explicitly forbids
discrimination against foreign subsidiaries.
Consequently, a firm with a foreign
subsidiary may appeal any discriminatory
treatment to the GATT/WTO in Geneva,
Switzerland. Its corporate income tax
cannot be higher than that of local
companies, it cannot be charged higher
duties to import intermediate goods, nor
be required to purchase inputs locally to
protect domestic production.
Chapter 5
Page 18
International taxation
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Income derived from foreign subsidiaries is
fully taxable at U.S. rates, but eligible for
tax credits on taxes deemed paid abroad
up to its marginal tax rate. A tax credit
thus typically reduces the tax liability of
the parent firm by the full amount paid in
foreign taxes. If the foreign corporate
rate is above 35%, a deferred tax credit is
given on the amount above 35% or is
combined with other sources of foreign
income less that 35% to reduce the rate to
an effective 35%.
Chapter 5
Page 19
International taxation
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A foreign sales corporation (FSC) allows
firms having export operations to enjoy
exemption of most export income from U.S.
taxes, even when the good is produced in
the U.S. Exempt foreign trade income
derives from “export property” sold, leased,
or rented outside the United States by the
FSC.
Profits not repatriated escape U.S.
taxation altogether, in violation of Article
VI Anti-Dumping of the GATT/WTO.
Chapter 5
Page 20
International taxation
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A foreign majority-controlled branch is
treated as part of the parent firm and
thus must repatriate profits and pay home
taxes contemporaneously.
A subsidiary incorporated locally need not
repatriate profits, nor pay home country
taxes unless it remits the profits.
Foreign income tax credits apply in both
cases.
The value-added tax and sales taxes are
deducted from income, and thus treated as
expenses.
Chapter 5
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International taxation: examples
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Country A, where the affiliate is located is
a high-tax country, so that the home
country, assumed to be the U.S., issues an
excess tax credit to the parent firm.
Chapter 5
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International taxation: examples
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Country B is a comparable tax country.
No U.S. taxes would be paid, the firm
receiving a full tax credit for the 35%
corporate income tax.
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International taxation: examples
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Country C is a low tax country.
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International taxation: examples
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The tax treatment of affiliates located in
Country D, a tax haven.
Chapter 5
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International taxation: examples
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A Foreign Sales Corporation located in a tax
haven benefits either from 34% exemption, or
17/23 exemption of foreign source income
depending on whether arm’s length pricing or
administrative rules pricing is applied. The
total exemption of foreign possessions source
income or possessions derived investment
income is also shown.
Chapter 5
Page 26
Working capital

A firm must have
operating balances to
manage its receivables,
inventories and payables.
Its net working capital
finances the cash
conversion cycle from
raw inputs to final
product and sale.
Chapter 5
Page 27
Cash netting
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If subsidiary A must pay 150 euros to
subsidiary C for widgets, and C must may
A 100 euros for intermediate inputs for
assembling widgets, rather than having two
separate transactions, subsidiary A (or a
centralized facility) can simply pay
subsidiary C 50 euros.
The single transaction nets the payment
saves the multinational firm transactions
and spread fees in its cash operations.
Chapter 5
Page 28
Mergers and acquisitions
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A merger is the absorption of one firm by
another. Firm A might acquire firm B by
offering two shares in A for each share of B.
B would then cease to exist. Typically, two
thirds of the voting shares of each firm must
approve the merger. In general, a merger is
only worthwhile is there is synergy in combining
the firms:
VAB  VA  VB

The value of the merged firm should be
greater than the individual firms taken alone.
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Mergers and acquisitions
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When firm A and firm B consolidate into a
new firm C, in general it should be true
that:
VC  V A  VB
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In practical terms, a consolidation is
equivalent to a merger.
Chapter 5
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Mergers and acquisitions
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Acquisition by cash
After the acquisition, the combined firms
are worth $170. Synergy is thus $20.
Firm A could acquire firm B by paying $60
in cash, a premium of $10 over its market
value in order to secure the 2/3 vote
necessary of B’s shareholders. Each share
would be tendered at $6 while it was
previously worth $5.
Chapter 5
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Mergers and acquisitions
Acquisition by cash
The value of Firm A after the acquisition
will therefore be $170 minus the $60 paid
to B’s stockholders. A is thus worth $110
after the acquisition, or:
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Chapter 5
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Mergers and acquisitions
Acquisition by shares
How many shares should A offer to B’s
shareholders? The correct amount would
equal the ratio: a170 = 60, giving them
shares worth $60. That is, a = 60/170 =
0.352941176 of the combined company.
an
and
nw
nw 
 10.90909
a
1  a 
n  nw

We can solve for the number of new shares
issued, n w , in addition to the exiting number
of shares, n = 20.
Chapter 5
Page 33
Mergers and acquisitions
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Acquisition by shares
Firm A’s situation is now:
The 10.91 shares offered to shareholders
of B are worth exactly $60 at the new
market price of $5.50!
Chapter 5
Page 34
Mergers and acquisitions
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Acquisition by shares and cash
Suppose firm A acquires firm by an offer
of both cash and stock, for instance, $30
in cash and the rest in stock.
How many shares of stock will firm A have
to offer? Firm A will therefore be worth
$140 after the cash payment of $30. In
this case a = 30/140 = .21428571429.
Chapter 5
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Mergers and acquisitions

Acquisition by shares and cash
 30 

20
140 

nw 
 5.45455
30 

1 

 140 

By offering exactly 5.45455 shares and
$30 in cash, Firm A would be offering the
same premium as with pure cash or pure
stock. Notice that the 5.45455 new
shares are worth exactly $30 at the new
share price of A, $5.5.
Chapter 5
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Mergers and acquisitions
Acquisition by shares and cash
Firm A’s new situation would be as follows:

Chapter 5
Page 37
Alternatives to acquisition
▪ Joint ventures involve local partners who share


in the managerial and financial decision-making
in the local venture.
Direct licensing agreements and management
contracts allow headquarters to share in some
of the profits from a locally owned operation.
Direct foreign investment should be considered
as an alternative.
A strategic alliance takes place when two firms
exchange stock and form a separate joint
venture to develop and manufacture a product
or service.
Chapter 5
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Offshore banking
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Offshore banking refers to deposits and loans
that are made in a country other than the
depositor’s or borrower’s country of origin.
Chapter 5
Page 39
Offshore banking
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The key differences between offshore banking
and domestic banking are the currency of
denomination, the tax jurisdiction and the
regulatory framework.
For accounts payable and hedging purposes, it
is often convenient to hold cash balances in a
foreign currency.
In some cases, however, offshore banking is
used for money-laundering.
Chapter 5
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An international business plan
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The principal ways of organizing a business are:

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A sole proprietorship involves an individual acting on his
or her own behalf in a business context.
A partnership formed by the independent action of the
partners whose rights and duties are spelled out in
business charters.
A limited partnership involves one or more investing
partners and at least one operating partner. An
investing partner is liable only to the extent of that
partner's investment.
A corporation is a single entity, a "person" that may
sue or be sued without its members being held liable.
Owners may enter or withdraw from the venture at any
time by buying or selling shares.
Chapter 5
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An international business plan
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The principal ways of terminating a business are:

Legal bankruptcy (Firms or creditors bring petitions
to a court for bankruptcy.)


In Chapter 7, or liquidation cases, the debtor's
property is sold off by a trustee to pay the debts
owed to creditors. An individual debtor can keep a
modest amount of household property or realty under
federal or state exemptions.
In Chapter 11, or business reorganization, the
business is continued by its management or a trustee
while creditors' claims are frozen pending approval
of a plan. With court approval, the plan can modify
or forgive debts, recapitalize a corporation, provide
for mergers or takeovers, or dispose of assets.
Chapter 5
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An international business plan

The profit-maximizing point: In operations,
setting marginal cost (the slope of the cost
curve) equal to marginal revenue (the slope of
the revenue curve) maximizes profits, p, the
difference between revenues and costs.
Chapter 5
Page 43
An international business plan
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The net present value of the firm is given by
substituting forecasted profits into the NPV
formula using the firm’s cost of borrowing, i,
to discount future cash flows:
NPV  p 0 
p1

p2
1  i  1  i 
2

p3
1  i 
3

p4
1  i 
4

p5
1  i 
5

T5
1  i 5
where T is the terminal value of the firm in
its fifth year. The terminal value is an
estimate of its resale value based on
discounted profits from the sixth year
onward. At worst, if the firm ceases
operations, it could be its scrap value.
Chapter 5
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The Aztec Café
▪ Let’s take the example of the Aztec Café whose
revenues and costs are in Mexican pesos. As a
start-up in 2001, its initial investment costs were
N$500,000 for the oven and new hood with fire
extinguisher, grease trap, tables, chairs and
dinnerware, plus renovation of the existing facility.
▪ The owner/manager, Juan Olive had borrowed from
a local bank the entire start up amount at 22% in
pesos, which gives us the weighted average cost of
capital (no equity was brought to the project).
▪ Juan elected straight line depreciation of his
investment over five years.
Chapter 5
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The Aztec Café
▪ Unfortunately, the business plan was done at the
end of the Aztec’s first year of operations in May
2001. Had it been done earlier, the project would
not have taken place.
▪ The Aztec’s forecasted revenue and costs yielded
a free cash flow projection for five years. In
addition, a terminal value was predicted as a nogrowth perpetuity of its fifth year’s free cash flow.
Chapter 5
Page 46
The Aztec Café
▪ In the first year, Juan accumulated arrears
in his rent, his loan and in payment of the 15%
value-added tax in Mexico. His cash-flow
was negative so he sought finance by running
arrears. The value of debt arrears had to be
subtracted from the net present value of
forecasted free-cash flow to value the
restaurant.
Chapter 5
Page 47
The Aztec Café
▪ The landlord could padlock the restaurant door at
any moment with a court order, and the lender could
seize the oven and equipment as secured collateral.
The state was about to file criminal charges for tax
evasion. The Aztec Café was clearly in serious
financial distress.
▪ Could it be sold? No, the restaurant had negative
net worth of $46,308. Its forecasted cash flow was
also negative.
▪ New equity financing was sought to recapitalize the
restaurant and re-pay the loan, rent and tax arrears.
Potential investors took the position was that any
more money put into the venture would be lost.
Chapter 5
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The Aztec Café
▪ The dénouement
▪ The Aztec Café was liquidated in June 2001.
▪ The owner turned in his keys to the landlord.
▪ The bank took the equipment and sold it in auction.
It also required the owner to sell his home, applying
the equity to the unpaid balance. It rescheduled the
remaining balance and penalties.
▪ Finally, he negotiated forgiveness of the arrears in
the value added tax.
▪ Moral of the story: look before you leap! That is,
do a reasoned business plan. Also, be wary of high
financial leverage, especially 100%.
Chapter 5
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Optimal international portfolio investment

Market and unique risk

Market risk, also known as systematic risk, represents
risk factors that are common to the whole economy. Firm
specific risk, also known as diversifiable risk, represent
risk factors that can be eliminated by diversification.
The variance of security i, i2 , can be written as the sum
of the market risk and the firm specific risk:
5.15
    
2
i
2
i
2
M
2
ei
where
 iM
  2
M
2
i
and  iM is the covariance between security i’s return and
the market return, and  M2 is the variance of the market
return.
Chapter 5
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Optimal international portfolio investment

Market and unique risk: the Beta
The beta, , of an individual security measures
the security’s sensitivity to market movements and
therefore is known as its market risk. For example,
the beta of the Standard and Poor’s 500 index
share should be about one since it reflects a
broad selection of market stocks. A riskier
security would have a beta greater than one, and
a less risky security would have a beta less than
one.
2

The e is the firm specific, diversifiable risk.
Chapter 5
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Optimal international portfolio investment

Portfolio diversification


The level of market risk is dealt with by choosing the betas
in the portfolio since the systematic risk is a weighted
average of the individual security betas. Systematic
variance equals  P2,m2 where  P is the simple average of the
individual security betas.
By choosing  P2, we decide the systematic variance of the
portfolio. A choice of domestic and international betas can
reduce systematic risk relative to a choice of only domestic
betas. In short, systematic risk is manipulated by choosing
the average beta of the securities, but the number of
securities does not matter.
Chapter 5
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Optimal international portfolio investment

Portfolio diversification

Non-systematic risk,  e2 ,is diversifiable by increasing the
number of securities. By sufficiently diversifying, the
investor can virtually eliminate firm-specific risk. By holding
both domestic and international securities, portfolio
diversification is more efficient since the universe of assets
is the choice set.
Chapter 5
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Optimal international portfolio investment

Portfolio diversification
Figure 5.7
Chapter 5
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Optimal international portfolio investment



Asset allocation with one domestic and one
foreign asset
Here we consider the allocation of the investment
budget between two risky funds, a domestic fund and
a foreign fund. If the proportion invested in the
domestic fund is wd , then the remainder is invested
in the international (g for global) fund,w g  1  wd .
Some basic relationships hold:
5.16
rP  wd rd  wg rg
• That is, the rate of return on the portfolio is a
weighted average of the rates of return on the
domestic and global funds.
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Optimal international portfolio investment



Asset allocation with one domestic and one
foreign asset
5.17
E rP   wd E rd   wg E rg 
That is, the expected rate of return on the
portfolio is a weighted average of the expected rates
of return on the domestic and global funds.
Chapter 5
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Optimal international portfolio investment

Asset allocation with one domestic and one
foreign asset
5.18
 P2  wd  d 2  wg  g 2  2wd  d wg  g  dg
That is, the variance of the portfolio is the sum of the
square of weighted volatilities plus a term involving the
correlation coefficient,  dg , between the domestic and the
global funds.
Chapter 5
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Optimal international portfolio investment
Figure 5.8
Chapter 5
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Optimal international portfolio investment

The efficient investment frontier
The efficient investment frontier is derived by
maximizing the expected return, subject to a given
risk. Alternatively, it can be derived by minimizing
the risk for a given expected rate of return on the
2
portfolio. For a given level of risk, P ,the efficient
weight of the global asset is given by:
5.19 w 
g

E rg  d2  E rd  g  d  dg


E rg   d2   g  d  dg  E rd   g2   g  d  dg
Chapter 5

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Optimal international portfolio investment

The efficient investment frontier
Note that this is the share of the global asset
necessary to be on the efficient investment frontier,
a purely technical condition. This share maximizes
expected portfolio return for each level of risk.
Our next step in the optimal efficient portfolio
analysis is to maximize the Sharpe “reward to risk”
ratio.
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Optimal international portfolio investment


The capital allocation line (CAL)
Investors may be risk averse, demanding a higher
rate of return - a risk premium - for holding risky
assets. Risk may be reduced either by converting
risky assets into safe assets such as money market
assets or by constructing a risky portfolio efficiently,
diversifying away unsystematic risk. Consider an
investor holding a risky portfolio, P, along with a
risk-free asset, T, such as US T-bills. The risky
portfolio consists of some domestic and some foreign
assets
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Optimal international portfolio investment

For example, a hypothetical portfolio might be:
IBM, US
Tiger International
(Portfolio P )
US T-bills (Portfolio T )
Complete portfolio (Portfolio C )
Assets
$50
30
80
Complete portfolio weights
0.5
0.3
0.8
20
0.2
100
1.0
Chapter 5
Risky portfolio weights
0.625
0.375
1.000
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Optimal international portfolio investment

This investor is holding 62.5% of her risky portfolio
in IBM, US and 37.5% of P in Tiger International.
Let w represent the holdings in US securities and w*
indicate the holdings of international securities in the
risky portfolio, so that w+w*=1. Thus, w=0.625 and
w*=0.375. The weight of the risky portfolio, P, in
the complete portfolio, C, including risk-free
investments is denoted by z. Thus the weight of the
risk-free asset in the complete portfolio is 1-z. Tbills represent 20% of the complete portfolio, or 1-z
= 0.2, and risky assets 80% of C, or z = 0.8. IBM,
US represents 50% of the complete portfolio and
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Tiger International 30%. Chapter 5
Optimal international portfolio investment


The investor is thus holding a risk-free asset and a bundle
of risky assets which can be thought of as one risky asset.
In this way, the investor can keep the relative shares of
the two risky assets constant in the risky portfolio P, and
at the same time reduce risk by selling them off
proportionately to acquire more of the risk-free asset,
Treasuries.
By changing the distribution of the risky asset relative to
the risk-free asset, yet maintaining the mix of assets in
the risky portfolio, the investor can reduce the risk of the
complete portfolio yet remain on the efficient investment
frontier. That is, z can be reduced in C while maintaining
w and w* fixed in P.
Chapter 5
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Optimal international portfolio investment

Portfolio expected return and risk

Notation:






rP
rf
Rate of return on the risky portfolio
Rate of return on the risk-free asset
ErP  Expected rate of return on the risky portfolio
The standard deviation (volatility) of the risky
portfolio
P
E r f   r f Expected rate of return on the risk-free asset
E rC  Expected rate of return on the complete portfolio
Chapter 5
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Optimal international portfolio investment



Consequently, with a fraction z of risky assets in the
portfolio and 1-z of risk-free assets, the rate of return
on the complete portfolio is:
5.20
rC  zrP  1  z r f
Consequently, the expected rate of return on the
complete portfolio is:

5.21
E rC   zE rP   1  z r f

5.23
E rC   r f  z E rP   r f



Or equivalently,
That is, the complete portfolio has a base return equal
the risk-free rate plus an expected market risk premium,
E rP   r f  on its exposure to risky assets, z.
Chapter 5
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Optimal international portfolio investment


Risk-averse investors demand a positive market risk
premium. The standard deviation of the complete
portfolio is indicated by:


5.24
C  z P
risk free asset is zero.
since the volatility of the
Chapter 5
Page 67
Optimal international portfolio investment

Substituting
z
C
into 5.23, we have:
P
 E rP   r f
E rC   r f  
 P


 C

which is the capital allocation line (CAL). Figure 5.9 plots
the capital allocation line (CAL) depicting the rise in
expected portfolio return against the standard deviation
of the risky asset.
Chapter 5
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Optimal international portfolio investment
Figure 5.9
Chapter 5
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Optimal international portfolio investment



The slope of the investment opportunity schedule is the
Sharpe “reward to risk” ratio:
5.25
E rP   r f
P
The slope is also called the reward-to-volatility ratio
since it is the ratio of the market risk premium to the
standard deviation of the risky portfolio.
Chapter 5
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Optimal international portfolio investment



Consider the following utility (happiness or choice)
function:
2
2 2
A

Az
P
C
5.26 U z   E rC  
 r f  z E rP   r f 
2
2


This investor enjoys higher expected return, E rC  , but
dislikes higher risk, C. The level of risk aversion is A
>0. The higher A, the more risk averse the investor.
Chapter 5
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Optimal international portfolio investment


Utility maximization: mathematically
The investor’s objective is to maximize utility (utils!) by
selecting the fraction, z, of the investment budget to be
invested in the risky portfolio, P. The expected return
and variance of the complete portfolio are E rC   r f  zE rP   r f 
2

and C respectively. To choose the best allocation to the
risky asset, we maximize utility, equation 5.26 with
respect to z. That is, maximize the quadratic utility
function with respect to z.
A C2
Az 2 P2
U z   E rC  
 r f  z E rP   r f 
2
2

Chapter 5

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Optimal international portfolio investment

Utility maximization: mathematically
yielding the optimal share of the risky portfolio in the
complete portfolio:
z 
E rP   r f
A P2
Where z* indicates the optimal share of the risky asset.
The optimal share of the risky asset:
• Rises with increases in the market risk premium, E rP   r f
• Falls with increases in the degree of risk aversion, A.
2

• Falls with increases in market volatility, P .

Chapter 5
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Optimal international portfolio investment


Utility maximization: graphically
Figure 5.10 illustrates the optimal allocation of assets for
a risk averse investor who chooses to hold approximately
half the portfolio in the risky asset and half in the safe
asset. This optimal allocation yields the highest level of
utility (at point C, the tangency of the capital allocation
line and the highest indifference curve).
Chapter 5
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Optimal investment decisions
▪ A risk averse investor mixes risk free Treasuries
with an efficient risky portfolio, thus maximizing her
utility:
Figure 5.10
Chapter 5
Page 75
Optimal investment decisions: an example
▪ For example, an investor might optimally hold half her
complete portfolio in risky assets:
z 
E rP   r f
A P2
0.15  0.05 0.10 1



2  0.10
0.20 2
where
▪ The market risk premium E rP   r f is 15%.
▪ Her degree of risk aversion, A, equals 2.
2

▪ Market variance, P , is 10%.
▪ The risk free rate, r f , is 5%.
Chapter 5
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Optimal investment decisions

Since the optimal portfolio of the individual investor
with average risk aversion, A*, is:

z 
E rP   r f
A

2
P
and the average global investor has z = 1, the risk
premium on the market portfolio is proportional to its
risk and average degree of risk aversion.
ErP   r f  A 

Chapter 5
2
P
Page 77
Application to China
The implication of this approach is that Chinese
investors will improve their efficient investment
frontier by diversifying into foreign securities.
They will increase their return and reduce their risk by
international portfolio diversification.
If Chinese investors were to hold one-fifth of their
portfolio in foreign assets, there would be a one-time
capital outflow of $1.4 trillion, approximately equal
to the entire foreign reserve holdings of the People’s
Bank of China.
Chapter 5
Page 78
Summary estimates for China
China, 2006/7
Market capitalization*
Money in circulation**
Total portfolio
USD, billions
2,300
4,515
6,815
International portfolio diversification rate
10%
$681 billion
20%
$1,363 billion
30%
$2,044 billion
* www.sinomania.com, May 2007.
** International Financial Statistics, December 2006.
From the standpoint of liberalizing the capital account
in China, large holdings of foreign exchange reserves
are certainly justifiable. Chapter 5
Page 79
Conclusion


The multinational firm and investor have
many decisions involving international
borrowing, investing, cash management,
mergers and acquisitions, and international
business planning.
The objective of this chapter is to provide a
framework for decision making and financial
management of the international business
firm.
Chapter 5
Page 80