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Colegio Mayor de Nuestra Señora del Rosario International Finance Professor: Alejandro José Useche Arévalo Colegio Mayor de Nuestra Señora del Rosario International Finance Professor: Alejandro José Useche Arévalo Monitor: Daniela Mc. Allister Harker April 2013

© This Power Point presentation is an academic tool, whose intelectual property is owned © This Power Point presentation is an academic tool, whose intelectual property is owned by its author, Alejandro José Useche Arévalo. It has been prepared as study guide for the International Finance class at Universidad del Rosario’s Economics Faculty. Any reproduction is forbidden.

 INTERNATIONAL DEBT FINANCING INTERNATIONAL DEBT FINANCING

CORPORATE SOURCES OF FUNDS General Sources of Funds: 1. Internally-generated cash 2. External funds CORPORATE SOURCES OF FUNDS General Sources of Funds: 1. Internally-generated cash 2. External funds • • Short-term external funds Long-term external funds

CORPORATE SOURCES OF FUNDS Forms of Securities: 1. Debt: the most preferred form 2. CORPORATE SOURCES OF FUNDS Forms of Securities: 1. Debt: the most preferred form 2. Equity Debt Instruments: 1. Commercial Bank Loans 2. Bonds a. b. Publicly issued Privately issued Capital structure

CURRENCY OF DENOMINATION ¢ ¢ When a purely domestic company issues debt denominated in CURRENCY OF DENOMINATION ¢ ¢ When a purely domestic company issues debt denominated in a foreign currency, it faces a foreign currency risk. For a multinational company it is natural to borrow in different currencies, because its revenues are also denominated in various currencies. Centralized debt denomination: when a multinational company denomination chooses to have all its debt in just one currency. Descentralized debt denomination: when a multinational denomination company borrows in the countries and currencies where its subsidiaries operate or to which it exports. In this case, it is possible to have a "balance-sheet hedge”.

CORPORATE SOURCES OF FUNDS Securitization: replacing bank Securitization loans with securities issued in public CORPORATE SOURCES OF FUNDS Securitization: replacing bank Securitization loans with securities issued in public markets. This process can reduce a company’s cost of capital (WACC).

Bonds ¢ A bond is a debt security, in which the authorized issuer owes Bonds ¢ A bond is a debt security, in which the authorized issuer owes the holder a debt and, depending on the terms of the bond, has to pay interest (the coupon) and to repay the principal (par value or face value) at a later date (maturity). ¢ Bonds provide the borrower with external funds to finance longterm investments, or, in the case of government bonds, to finance current expenditure.

Bonds: properties ¢ Bonds and stocks are both securities, but the major difference between Bonds: properties ¢ Bonds and stocks are both securities, but the major difference between them is that stockholders have an equity stake in the company (i. e. , they are owners), whereas bondholders have a creditor stake in the company (i. e. , they are lenders). Another difference is that bonds have a defined maturity, after which the bond is redeemed, whereas stocks may be outstanding indefinitely. An exception is a consol bond, which is a perpetuity. ¢ The bondholder receives a set amount, known in advance, no matter what happens to interest rates, stock prices, and so on. ¢ Instead of the coupon responding to a change in the interest rate, it is the price of the bond that changes: the bond is worth less when interest rates rise. 9

The World’s Bond Markets ¢ ¢ Bond traders at the Chicago Board of Trade The World’s Bond Markets ¢ ¢ Bond traders at the Chicago Board of Trade The total market value of the world’s bond markets are about 50% larger than the world’s equity markets. Most issues are denominated in EUR, USD, GBP and JPY.

International bonds by nationality of issuer Countries Amounts outstanding (billion USD) Dec 2010 Dec International bonds by nationality of issuer Countries Amounts outstanding (billion USD) Dec 2010 Dec 2011 %world (2011) All countries 26. 775, 2 27. 819, 7 Developed countries Developing countries 24. 093, 5 1. 532, 4 24. 570, 2 1. 739, 4 88, 32% 6, 25% 7. 072, 7 3. 027, 1 2. 625, 2 1. 879, 4 1. 723, 1 1. 318, 5 647, 5 172, 4 105, 1 72, 9 53, 8 48, 6 24, 2 23, 9 7. 302, 7 3. 017, 4 2. 606, 7 1. 985, 2 1. 812, 2 1. 327, 9 694, 3 203, 8 122, 4 118, 6 54, 8 59, 0 28, 8 28, 5 26, 25% 10, 85% 9, 37% 7, 14% 6, 51% 4, 77% 2, 50% 0, 73% 0, 44% 0, 43% 0, 20% 0, 21% 0, 10% United States United Kingdom Germany France Spain Italy Canada Brazil Mexico China Argentina Venezuela Colombia Israel Source: own calculations based on BIS Quarterly Review, March 2012

International bonds by currency of issue Source: own calculations based on BIS Quarterly Review, International bonds by currency of issue Source: own calculations based on BIS Quarterly Review, March 2012

ZERO COUPON BONDS: Pure discount bonds or zeros are sold at a large discount ZERO COUPON BONDS: Pure discount bonds or zeros are sold at a large discount from face value because there is no cash flow until maturity. v Advantage: you can invest relatively smaller amounts and choose maturity Advantage dates to coincide with times you know you will need the money. v Drawback: income taxes are due annually on the interest that accrues, Drawback even though you don’t receive the actual payment until the bond matures. Another drawback is that they are volatile in the secondary market. COUPON BONDS: Debt obligations with coupons attached that represent periodic (usually semiannual) interest payments.

v BEARER BONDS: Bonds with no registered owner, they offer anonymity but they also v BEARER BONDS: Bonds with no registered owner, they offer anonymity but they also offer the same risk of loss as currency. v REGISTERED BONDS: the owner’s name is registered with the issuer. v CALLABLE BONDS: They allow the issuer to retire a bond before it BONDS: matures. v DUAL-CURRENCY BONDS: A straight fixed-rate bond, with interest BONDS: paid in one currency, and principal in another currency.

v ASSET-BACKED SECURITIES: bonds whose interest and principal payments are backed by underlying cash v ASSET-BACKED SECURITIES: bonds whose interest and principal payments are backed by underlying cash flows from other assets; for example, mortgage-backed securities (MBS's), collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs). v SUBORDINATED BONDS: those that have a lower priority than “senior” bonds in case of liquidation or bankruptcy of the issuer. As a result, the risk is higher but therefore they offer also a higher rate. v PERPETUAL BONDS: perpetuities or “Perps” have no maturity date, as the famous “UK Consols”. West Shore Railroad company issued a bond which matures in 2361, which is virtually a perpetuity from a financial point of view, with the current value of principal near zero.

Most common types of bonds traded in international markets Ø Straight Fixed Rate Debt Most common types of bonds traded in international markets Ø Straight Fixed Rate Debt Ø Floating-Rate Notes Ø Equity-Related Bonds

Most common types of bonds traded in international markets 1. STRAIGHT FIXED RATE DEBT: Most common types of bonds traded in international markets 1. STRAIGHT FIXED RATE DEBT: v v “Plain vanilla” or “level coupon bonds” with a specified coupon rate and maturity, and no options attached. Usually: annual or semi-annual coupon payment. 2. FLOATING-RATE NOTES (FRN): v v Medium term bonds with coupon payments indexed to some reference rate. Common reference rates are 3 -month and 6 -month LIBOR. 3. EQUITY-RELATED BONDS: v v Convertibles: Convertible bonds allow the holder to surrender his bond in exchange for a specified number of shares in the firm of the issuer. Bonds with equity warrants: They allow the holder to keep bonds but still buy a specified number of shares in the firm of the issuer at a specified price. These are straight fixed rate bonds with a call option for a number of shares at a strike price over a period of time.

International bonds by type and sector Source: own calculations based on BIS Quarterly Review, International bonds by type and sector Source: own calculations based on BIS Quarterly Review, March 2012

International Bonds v FOREIGN BOND: issued by a foreign borrower to investors in BOND International Bonds v FOREIGN BOND: issued by a foreign borrower to investors in BOND another country and denominated in the currency of that country. Example: Yankee bond issued in the United States by a foreign agent, denominated in US dollars. v EUROBOND: denominated in a specific currency, but sold to EUROBOND investors in a capital market other than the country of the denominated currency. v GLOBAL BONDS: Sold simultaneously on several markets in : the currency of each market, it is a very large international bond offering by a single borrower, mostly institutional investors are the purchasers so far.

Foreign Bonds: Nicknames Foreign Bonds: Nicknames

US Government Bonds: Treasuries v Technically, T-bills are not bonds because of their short US Government Bonds: Treasuries v Technically, T-bills are not bonds because of their short maturity. v All debt issued by USA is regarded as extremely safe (“risk-free”), as is the debt of any developed and stable country; however, the debt of many countries carries substantial default risk.

U. S. Department of the Treasury http: //www. treasury. gov/resource-center/data-chart-center/interestrates/Pages/Text. View. aspx? data=yield Wall U. S. Department of the Treasury http: //www. treasury. gov/resource-center/data-chart-center/interestrates/Pages/Text. View. aspx? data=yield Wall Street Journal http: //online. wsj. com/mdc/public/page/2_3022 -govtbonds. html

v TIPS: Treasury Inflation Protected Securities, issued with maturities of TIPS five, 10 and v TIPS: Treasury Inflation Protected Securities, issued with maturities of TIPS five, 10 and 30 years. TIPS shelter investors from inflation risk because their principal is adjusted semiannually for inflation based on changes in the Consumer Price Index-Urban Consumers (CPI-U). v STRIPS: Separate Trading of Registered Interest and Principal of STRIPS: Securities. The STRIPS program lets investors hold and trade the individual interest and principal components of eligible Treasury notes and bonds as separate securities. v STRIPPED BONDS: Making a series of zero coupon bonds from a single coupon bond; the coupons and the maturity value are stripped and sold separately as zero coupon bonds.

International Bond Market Instruments: Summary Instrument Frequency of Payment Size of Coupon Payoff at International Bond Market Instruments: Summary Instrument Frequency of Payment Size of Coupon Payoff at Maturity Straight Fixed-Rate Annual Fixed Currency of issue Floating Rate Note Every 3 or 6 months Variable Currency of issue Convertible Bond Annual Fixed Straight fixed rate with equity warrants Annual Fixed Zero none zero Currency of issue or conversion to equity shares. Currency of issue plus conversion to equity shares. Currency of issue Dual Currency Bond Annual Fixed Dual currency

Comparative characteristics of bonds issues Comparative characteristics of bonds issues

Bond transactions ¢ Primary Market: new issues l The primary market is that part Bond transactions ¢ Primary Market: new issues l The primary market is that part of the capital markets that deals with the issue of new securities. The process of selling new issues to investors is called underwriting. In the case of a new stock issue, this sale is an initial public offering (IPO). Dealers (most of all investment banks) earn a commission that is built into the price of the security offering, they usually use own funds to buy new issue at a discount from the issue price. ¢ Secondary Market: “used” issues = resale l The secondary market or aftermarket is the financial market where previously issued securities are bought and sold. Most bonds and structured products trade “over the counter, ” or by phoning the bond desk of one’s broker-dealer.

Bond Valuation ¢ After issue, a bond is traded on the market at a Bond Valuation ¢ After issue, a bond is traded on the market at a price which reflects the current level of interest rates and the degree of risk associated with the bond. Typically we are interested in calculating either the market price that a bond should sell for, given that the investor wants to obtain a particular market yield; or the effective yield (yield to maturity), given maturity the price at which the bond is trading. ¢ The value of a financial security is the PV of expected future cash flows to value bonds we need to estimate future cash flows (size and timing) and discount at an appropriate rate. Value = present value of all expected future cash flows Value Present Value of a Bond = Present Value of the Coupon Payments + Present Value of the Par Value

Bond Valuation Bond Valuation

Accrued Interest ¢ Accrued interest is the interest that adds up (accrues) each day Accrued Interest ¢ Accrued interest is the interest that adds up (accrues) each day between coupon payments. ¢ If you trade a bond in the secondary market, you most likely will catch the bond between coupon payment dates. ¢ If you're selling, you're entitled to the price of the bond, plus the accrued interest that the bond has earned up to the sale date. ¢ The buyer compensates you for this portion of the coupon interest, which is generally handled by adding the amount to the contract price of the bond.

Clean & dirty prices v When the bond is not valued precisely on a Clean & dirty prices v When the bond is not valued precisely on a coupon date, the calculated price will incorporate accrued interest. v The price of a bond which includes this accrued interest is known as the "dirty price" (or "full price" or "all in price" or "Cash price"). The "clean price" is the price excluding any interest that has accrued. v v

Determining Day Count ¢ Actual/actual day count: used for Treasury securities. This method counts Determining Day Count ¢ Actual/actual day count: used for Treasury securities. This method counts the exact number of days until the next payment. ¢ 30/360 day count: used for corporate bonds. This count convention assumes that a year consists of 360 days and each month consists of 30 days.

Bond Valuation Bond Valuation

Yield to Maturity v YTM is the discount rate which equates the price of Yield to Maturity v YTM is the discount rate which equates the price of a bond with the Present Value of its expected future cash flows: in other words, its Internal Rate of Return. v Example: what is the yield to maturity of a 5% coupon 9 year $1, 000 par value bond if the price is $813 (annual coupons)? We need to solve the following equation for r :

Reading a Corporate Bond Table ¢ High, Low, Last: the intraday (if real-time) or Reading a Corporate Bond Table ¢ High, Low, Last: the intraday (if real-time) or previous day's prices at which the bond traded. ¢ Prices below 100 are trading at a discount to par, and those above 100 are trading at premium to par. ¢ Change: change in price from the previous price at which the bond traded. ¢ % Yield: annual percentage rate of return an investor will receive until the bond matures (Yield-to-Maturity or YTM) or is called (Yield-to-Call or YTC). The Yield-to-Worst (YTW), which is the lower of the YTC or YTM, is also used frequently. ¢ When a bond is trading at a premium (above 100), a bond's yield is less than its coupon. When a bond is trading at a discount (below 100), the bond's yield is more than its coupon.

International Bond Market Credit Ratings v v v Standard & Poor’s, Fitch IBCA, Moody’s International Bond Market Credit Ratings v v v Standard & Poor’s, Fitch IBCA, Moody’s and DBRS sell credit rating analysis. Ratings focus on default risk, not exchange rate risk. Assessing sovereign government debt focuses on political risk debt and economic risk. Economic risk: external debt, BOP flexibility, economic structure & growth, management of the economy, and economic prospects. JUNK BOND: A bond rated 'BB' or lower because of its high default risk. Also known as a "high-yield bond" or "speculative bond". These are usually purchased for speculative purposes.

Colombia’s S&P Rating Raised on Economic Growth, Peace Talks Source: www. bloomberg. com ¢ Colombia’s S&P Rating Raised on Economic Growth, Peace Talks Source: www. bloomberg. com ¢ ¢ Colombia’s foreign debt rating was raised to BBB by Standard & Poor’s as economic growth increased tax revenue and peace talks with rebels boosted investor confidence. Yields on benchmark local bonds fell to a record low as S&P lifted Colombia one step to BBB with a stable outlook. The rating is in line with Brazil, Mexico and Peru. “A stronger fiscal profile, growing domestic capital markets, and favorable longterm prospects for GDP growth have strengthened Colombia’s creditworthiness”. “The rating upgrade will allow lower borrowing costs in Colombia, Finance Minister Mauricio Cardenas told reporters today. “This is very positive, ” Cardenas said. “It’s the best economic news we’ve had this year. ” The yield on Colombia’s benchmark peso bond due in 2024 dropped four basis points, or 0. 04 percentage point, to 4. 84 percent, the lowest closing level since the securities were issued in 2009. The extra yield that investors demand to own Colombian government dollar bonds instead of U. S. Treasuries was unchanged at 133 basis points at 3: 04 p. m. in New York, according to JPMorgan Chase & Co. ’s EMBI Global index.

S&P Credit Ratings http: //www. standardandpoors. com/ratings/definitions-and-faqs/en/us AAA: Extremely strong capacity to meet financial S&P Credit Ratings http: //www. standardandpoors. com/ratings/definitions-and-faqs/en/us AAA: Extremely strong capacity to meet financial commitments. Highest Rating. AAA AA: Very strong capacity to meet financial commitments. AA A: Strong capacity to meet financial commitments, but somewhat susceptible to adverse economic conditions and changes in circumstances. BBB: Adequate capacity to meet financial commitments, but more subject to BBB adverse economic conditions. BBB-: Considered lowest investment grade by market participants. BBBBB+: Considered highest speculative grade by market participants. BB+: BB: Less vulnerable in the near-term but faces major ongoing uncertainties to BB adverse business, financial and economic conditions. B: More vulnerable to adverse business, financial and economic conditions but currently has the capacity to meet financial commitments. CCC: Currently vulnerable and dependent on favorable business, financial and CCC economic conditions to meet financial commitments. CC: Currently highly vulnerable. CC C: Currently highly vulnerable obligations and other defined circumstances. D: Payment default on financial commitments. ¢ Note: Ratings from ‘AA’ to ‘CCC’ may be modified by the addition of a plus (+) or minus (-) sign to show relative standing within the major rating categories.

Emerging Markets Bond Index (EMBI) ¢ A benchmark index for measuring the total return Emerging Markets Bond Index (EMBI) ¢ A benchmark index for measuring the total return performance of international government bonds issued by emerging market countries, issued in something other than local currency. ¢ The most popular indexes are the J. P. Morgan Emerging Bond Index (EMBI) and EMBI+; the latter measures both Brady bonds and other sovereign debt while the EMBI measures only Brady bonds. ¢ The EMBI+ is a market capitalization-weighted index and is rebalanced on the last business day of each month. Only issues with a current face amount outstanding of $500 million or more and a remaining life of greater than 2 1/2 years are eligible for inclusion in the index. Index returns are available hedged or unhedged in a variety of currencies.

Emerging Markets Bond Index (EMBI) April 2013 / Source: www. cesla. com Country Latest Emerging Markets Bond Index (EMBI) April 2013 / Source: www. cesla. com Country Latest 3 months ago 1 year ago Argentina 1216 966 900 Brasil 175 134 183 Chile 145 122 150 Colombia 132 107 149 Ecuador 702 792 México 677 171 169 182 Perú 130 156 160 Venezuela 825 722 899 EMBI + indicates the spread over the US Treasury Bonds that a country’s sovereign bond must pay in order to raise funds, expressed in basis points.

Yield curves ¢ Relationship between a particular yield measure and a bond’s maturity; also Yield curves ¢ Relationship between a particular yield measure and a bond’s maturity; also called term structure of interest rates. ¢ To construct it, only homogeneous bonds should be included: same risk, same liquidity.

¢ Raising yield curve: typical ¢ Flat term structure ¢ Inverted yield curve ¢ Raising yield curve: typical ¢ Flat term structure ¢ Inverted yield curve

Yield curve – Colombia (Sovereign) Yield curve – Colombia (Sovereign)

Yield curve – Greece (Sovereign) Yield curve – Greece (Sovereign)

Convexity ¢ For any given bond, a graph of the relationship between price and Convexity ¢ For any given bond, a graph of the relationship between price and yield is convex. This means that the graph forms a curve rather than a straight-line (linear). ¢ The degree to which the graph is curved shows how much a bond's yield changes in response to a change in price. In this section we take a look at what affects convexity and how investors can use it to compare bonds.

Convexity 500 Convexity 500

Duration ¢ It is a measurement of how long, in years, it takes for Duration ¢ It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.

Duration ¢ Duration increases immediately on the day a coupon is paid, but throughout Duration ¢ Duration increases immediately on the day a coupon is paid, but throughout the life of the bond, the duration is continually decreasing as time to the bond's maturity decreases. ¢ The formula usually used to calculate a bond's basic duration is the Macaulay duration, which was created by Frederick Macaulay: it is calculated by adding the results of multiplying the present value of each cash flow by the time it is received and dividing by the total price of the security. N Macaulay Duration = wj tj j=1 where: t 1, t 2, … = dates of each Cash Flow w 1, w 2, … = weight of each Cash Flow = present value of each CF / total present value of all CF

Macaulay Duration MACAULAY DURATION Nominal value Coupon Time to maturity Coupon yield Market interest Macaulay Duration MACAULAY DURATION Nominal value Coupon Time to maturity Coupon yield Market interest rate tj CFj 0 1 2 3 4 5 6 CFj / (1+im )^j -1000 360 360 360 1360 257, 14 183, 67 131, 20 93, 71 66, 94 180, 62 913, 28 1000 Annual 6 36% 40% wj 0, 2816 0, 2011 0, 1437 0, 1026 0, 0733 0, 1978 1, 00 wj tj 0, 2816 0, 4022 0, 4310 0, 4104 0, 3665 1, 1866 3, 08 Duration

Duration of a portfolio of bonds ¢ Assuming a flat term structure, the duration Duration of a portfolio of bonds ¢ Assuming a flat term structure, the duration of a portfolio of bonds is the weighted average ot its individual durations. Portfolio’s value: P = Σ αj Pj If α < 0 : short position ¢ ¢ Portfolio’s duration: Dp = Σ Dj αj Pj/P

Modified Duration v It is a modified version of the Macaulay model that accounts Modified Duration v It is a modified version of the Macaulay model that accounts for changing interest rates: as fluctuating interest rates will affect duration, this modified formula shows how much the duration changes for each percentage change in yield. v The formula is appropriate for investors wishing to measure the volatility of a particular bond. v Wall Street Journal: Ryan Indexes http: //online. wsj. com/mdc/public/page/2_3022 -bondmkt. html

Modified Duration ¢ ¢ ¢ Zero-copupon bond Time to maturity: 1 year Yield: 30, Modified Duration ¢ ¢ ¢ Zero-copupon bond Time to maturity: 1 year Yield: 30, 21% Macaulay Duration = 1 Modified Duration = Duration / (1+i) = 1 / 1, 3021 = 0, 77 Modified Duration If market interest rate increases in 1%, bond’s price will decrease 0, 77%.

Duration & Convexity ¢ If we graph a tangent at a particular price of Duration & Convexity ¢ If we graph a tangent at a particular price of the bond (touching a point on the curved price-yield curve), the linear tangent is the bond's duration, which is shown in red on the graph. The exact point where the two lines touch represents Macaulay duration. ¢ Modified duration must be used to measure how duration is affected by changes in interest rates. But modified duration does not account for large changes in price. If we were to use duration to estimate the price resulting from a significant change in yield, the estimation would be inaccurate. The yellow portions of the graph show the ranges in which using duration for estimating price would be inappropriate.

Immunization ¢ Strategy used to minimize the interest rate risk of bond investments by Immunization ¢ Strategy used to minimize the interest rate risk of bond investments by adjusting the investor's time horizon to match the bond’s duration. ¢ Example: an investor needs $10. 000 in two years; she can “immunize” Example her bond portfolio by selecting bonds that will equal exactly $10. 000 in two years regardless of interest rate changes she can buy one zerocoupon bond that will mature in two years to equal $10. 000, or several coupon bonds each with a two year duration, or several bonds with a twoyear "average" duration. ¢ The duration of the assets is matched with the duration of the liabilities; to make the match more profitable, it must be assured that the convexity of the assets exceed the convexity of the liabilities.

Example: 5 -year annual coupon bond Example Nominal value Coupon rate Market rate = Example: 5 -year annual coupon bond Example Nominal value Coupon rate Market rate = $100 = 13, 77% = 10, 00%

If the bond is bought today and sold in the precise moment of its If the bond is bought today and sold in the precise moment of its duration, its value in that moment of time will be virtually the same, whatever happens to interest rates:

Selecting the currency of issue ¢ In order to raise funds, an issuer can Selecting the currency of issue ¢ In order to raise funds, an issuer can choose between selling bonds in the domestic market or in a foreign market. ¢ Just as taking a loan, this decision depends on the difference between the domestic interest rate that she will pay to the bondholders, and the foreign interest rate adjusted by the depreciation or appreciation. ¢ Example: Is it better for Inverargos to issue bonds in the Colombian or in the German market? Issuer Inverargos S. A. Amount needed COP 500 million Time to maturity 5 years Yield for Colombian bonds 10% Yield for German bonds 5% Spot exchange rate 2500 COP per EUR 5 -year forward exchange rate 3400 COP per EUR

Selecting the currency of issue Coca-Cola wishes to raise $1 billion. The company can Selecting the currency of issue Coca-Cola wishes to raise $1 billion. The company can issue USD or GBP denominated bonds. For simplicity, assume all payments are made at maturity. USD (billions) GBP (billions) Initial amount raised 1 1 / S Principal payment [ 1+r ] n [ 1+r* ] n / S where S = exchange rate, in American quotes. Coca-Cola will choose the GBP as the currency of issue only if: [ 1+r ]n > [ 1+r* ]n [ 1+ ΔE/E ] / S