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Chapter 5 1 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University of Miami Michael Connolly © 2007

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Page 1: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 1

International Financial ManagementChapter 5 International financial

management

Michael ConnollySchool of Business Administration,

University of Miami

Michael Connolly © 2007

Page 2: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 2

Summary

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

Page 3: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 3

Capital structure

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

Page 4: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 4

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).

where WACC indicates the weighted average cost of capital, the cost of debt, D, the cost of equity, E, and the marginal corporate tax rate.

ED

ER

ED

DtRWACC EcD 1

DR

ER ct

Page 5: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 5

Capital structure 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:

Your firm should use this rate to discount future cash flows.

7.0%143.035.01%10%05.11

Page 6: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 6

Capital structure

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.

Page 7: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 7

Capital structure

Consequently, there is an optimum capital structure which minimizes the weighted average cost of capital

Page 8: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 8

International capital structure

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

US

UK

R

R

WACC

WACC

1

1

1

1

$

£

11

11 $£

US

UK

R

RWACCWACC

Page 9: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 9

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:

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.

.

1045.1

03.11105.1%9.10

Page 10: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 10

Crosslisting on foreign stock exchanges

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.

Page 11: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 11

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.

Page 12: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 12

Transfer pricing 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.

Page 13: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 13

Transfer pricing 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:

Where represents the transfer price,

the price at which the firm purchases the input on the external market, and the elasticity of supply of the intermediate input to the marketing division.

1

1x

t

P

P

tP xP

Page 14: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 14

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 thisabuse of transfer pricing.

Page 15: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 15

Transfer pricing 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.

where is the absolute value of the elasticity of market demand for the intermediate good.

1

1 x

t

P

P

Page 16: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 16

Transfer pricing For example, if = 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, approaches infinity, and the optimal transfer price equals the market price of the intermediate good.

Page 17: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 17

International taxation 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.

Page 18: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 18

International taxation 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.

Page 19: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 19

International taxation 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%.

Page 20: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 20

International taxation 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.

Page 21: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 21

International taxation 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.

Page 22: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 22

International taxation: examples 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.

Page 23: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 23

International taxation: examples 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.

Page 24: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 24

International taxation: examples Country C is a low tax country.

Page 25: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 25

International taxation: examples The tax treatment of affiliates located

in Country D, a tax haven.

Page 26: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 26

International taxation: examples 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.

Page 27: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 27

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.

Page 28: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 28

Cash netting 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.

Page 29: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 29

Mergers and acquisitions 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:

The value of the merged firm should be greater than the individual firms taken alone.

BAAB VVV

Page 30: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 30

Mergers and acquisitions When firm A and firm B consolidate

into a new firm C, in general it should be true that:

In practical terms, a consolidation is equivalent to a merger.

BAC VVV

Page 31: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 31

Mergers and acquisitions 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.

Page 32: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 32

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:

Page 33: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 33

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.

and

We can solve for the number of new shares issued, , in addition to the exiting number of shares, n = 20.

w

w

nn

na

90909.10

1

a

annw

wn

Page 34: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 34

Mergers and acquisitions 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!

Page 35: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 35

Mergers and acquisitions 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.

Page 36: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 36

Mergers and acquisitions Acquisition by shares and cash

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.

45455.5

140

301

20140

30

wn

Page 37: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 37

Mergers and acquisitions Acquisition by shares and cash Firm A’s new situation would be as

follows:

Page 38: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 38

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.

Page 39: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 39

Offshore banking Offshore banking refers to deposits and

loans that are made in a country other than the depositor’s or borrower’s country of origin.

Page 40: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 40

Offshore banking 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.

Page 41: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 41

An international business plan The principal ways of organizing a business are:

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.

Page 42: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 42

An international business plan 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.

Page 43: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 43

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, , the difference between revenues and costs.

Page 44: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 44

An international business plan 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:

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.

55

55

44

33

221

0111111 i

T

iiiiiNPV

Page 45: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 45

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.

Page 46: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 46

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 no-growth perpetuity of its fifth year’s free cash flow.

Page 47: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 47

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.

Page 48: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 48

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.

Page 49: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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%.

Page 50: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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, , can be written as the sum of the market risk and the firm specific risk:

5.15 where

and is the covariance between security i’s return and the market return, and is the variance of the market return.

2222

ieMii 2

2

M

iMi

2i

2M

iM

Page 51: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 51

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.

The is the firm specific, diversifiable risk.

2e

Page 52: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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 , where is the simple average of the individual security betas.

By choosing , 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.

22mP P

2P

Page 53: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Portfolio diversification Non-systematic risk, ,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.

2e

Page 54: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Portfolio diversification

Figure 5.7

Page 55: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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 , then the remainder is invested in the international (g for global) fund, .

Some basic relationships hold:

5.16

• That is, the rate of return on the portfolio is a weighted average of the rates of return on the domestic and global funds.

dg ww 1dw

ggddP rwrwr

Page 56: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Asset allocation with one domestic and one foreign asset

5.17

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.

ggddP rEwrEwrE

Page 57: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Asset allocation with one domestic and one foreign asset

5.18

That is, the variance of the portfolio is the sum of the square of weighted volatilities plus a term involving the correlation coefficient, , between the domestic and the global funds.

dgggddggddP wwww 2222

dg

Page 58: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 58

Optimal international portfolio investment

Figure 5.8

Page 59: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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 portfolio. For a given level of risk, ,the efficient weight of the global asset is given by:

5.19

dgdggddgdgdg

dgdgddgg rErE

rErEw

22

2

2P

Page 60: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 60

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.

Page 61: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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

Page 62: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

For example, a hypothetical portfolio might be:

Assets Complete portfolio weights Risky portfolio weightsIBM, US $50 0.5 0.625Tiger International 30 0.3 0.375(Portfolio P ) 80 0.8 1.000

US T-bills (Portfolio T ) 20 0.2

Complete portfolio (Portfolio C ) 100 1.0

Page 63: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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. T-bills 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 Tiger International 30%.

Page 64: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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.

Page 65: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Portfolio expected return and risk Notation: Rate of return on the risky portfolio Rate of return on the risk-free asset Expected rate of return on the risky

portfolio The standard deviation (volatility) of the

risky portfolio Expected rate of return on the risk-free asset

Expected rate of return on the complete portfolio

Pr

fr

PrE

P

ff rrE

CrE

Page 66: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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 Consequently, the expected rate of return on the

complete portfolio is: 5.21 Or equivalently, 5.23 That is, the complete portfolio has a base return

equal the risk-free rate plus an expected market risk premium, on its exposure to risky assets, z.

fPC rzzrr 1

fPC rzrzErE 1

fPfC rrEzrrE

fP rrE

Page 67: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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 since the volatility of the risk free asset is zero.

PC z

Page 68: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Substituting into 5.23, we have:

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.

P

Cz

C

P

fPfC

rrErrE

Page 69: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Figure 5.9

Page 70: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

The slope of the investment opportunity schedule is the Sharpe “reward to risk” ratio:

5.25

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.

P

fP rrE

Page 71: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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Optimal international portfolio investment

Consider the following utility (happiness or choice) function:

5.26

This investor enjoys higher expected return, , but dislikes higher risk, . The level of risk aversion is A >0. The higher A, the more risk averse the investor.

22

222P

fPfC

C

AzrrEzr

ArEzU

CrEC

Page 72: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

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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 and 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.

22

222P

fPfC

C

AzrrEzr

ArEzU

fPfC rrEzrrE 2C

Page 73: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 73

Optimal international portfolio investment

Utility maximization: mathematically

yielding the optimal share of the risky portfolio in the complete portfolio:

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,• Falls with increases in the degree of risk aversion,

A.• Falls with increases in market volatility, .

2P

fP

A

rrEz

fP rrE

2P

Page 74: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 74

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).

Page 75: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 75

Optimal investment decisions

▪ A risk averse investor mixes risk free Treasuries with an efficient risky portfolio, thus maximizing her utility:

Figure 5.10

Page 76: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 76

Optimal investment decisions: an example

▪ For example, an investor might optimally hold half her complete portfolio in risky assets:

where

▪ The market risk premium is 15%.

▪ Her degree of risk aversion, A, equals 2.

▪ Market variance, ,is 10%.

▪ The risk free rate, , is 5%.

fP rrE

2P

2

1

20.0

10.0

10.02

05.015.02

P

fP

A

rrEz

fr

Page 77: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 77

Optimal investment decisions Since the optimal portfolio of the individual

investor with average risk aversion, A*, is:

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.

2P

fP

A

rrEz

2PfP ArrE

Page 78: Chapter 51 International Financial Management Chapter 5 International financial management Michael Connolly School of Business Administration, University

Chapter 5 Page 78

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.

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Summary estimates for China

USD, billionsMarket capitalization* 2,300Money in circulation** 4,515

Total portfolio 6,815

International portfolio diversification rate10% $681 billion 20% $1,363 billion 30% $2,044 billion

* www.sinomania.com, May 2007.** International Financial Statistics, December 2006.

China, 2006/7

From the standpoint of liberalizing the capital accountin China, large holdings of foreign exchange reservesare certainly justifiable.

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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.