CURRENCY CHOICES IN VALUATION AND THE INTEREST PARITY AND PURCHASING POWER PARITY THEORIES DR. GUILLERMO L. DUMRAUF

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1 CURRENCY CHOICES IN VALUATION AN THE INTEREST PARITY AN PURCHASING POWER PARITY THEORIES R. GUILLERMO L. UMRAUF

2 TO VALUE THE INVESTMENT IN THE OMESTIC OR FOREIGN CURRENCY? Valuing an invesmen or an acquisiion in a foreign or an emerging marke: wha currency should be used and how i affecs he inpus? Ofen he senior managemen is required o express expeced cash flows in a srong currency, usually dollars We are going o demonsrae he equivalence independen of he currency used in he valuaion, using an arbirage-free pricing model o obain he fair value of he business. 2

3 TO VALUE THE INVESTMENT IN THE OMESTIC OR FOREIGN CURRENCY? Two alernaive mehods can be used o obain a fair value: Forecas boh cash flows and cos of capial in dollars, esimaing he iscouned Cash Flow (CF) value in dollars. Forecas boh cash flows and cos of capial in domesic currency, esimaing he CF value in domesic currency. For he firs case, since he business generae sales, expenses, and cash flows in domesic currency, i is necessary o forecas he exchange rae for he invesmen horizon. In he second, we have o make some adjusmens in he cos of capial and long-erm growh rae used o esimae he erminal value of forecased cash flow. If he exchange rae and inflaion rae are forecased consisenly, boh mehodologies yield idenical values. 3

4 TO VALUE THE INVESTMENT IN THE OMESTIC OR FOREIGN CURRENCY? Esablishing he correc assumpions and selecing he economic heories ha provide raionale is required since he choice of currency affecs he inpus. The equivalence can be demonsraed using a CF model which assumes he simulaneous fulfillmen of Ineres Rae Pariy heory (IRP) and Purchasing Power Pariy heory (PPP). Cash flows and he cos of capial have o be esimaed consisenly in he same currency. 4

5 INTEREST RATE PARITY THEORY IRP saes a relaionship beween he ineres raes and he currency exchange raes. In he absence of arbirage opporuniies, he ineres rae differenial is equivalen o he differenial beween he spo and forward exchange raes, so he IRP mus hold for every period of in equilibrium: F S / US / US 1 i 1 i US Ineres rae differenial i US i US F / = one period forward domesic ineres rae, = one period forward dollar ineres rae, = forward exchange rae for one period forward. Therefore, he forward exchange rae can be expressed as: F / US S / US 1 i 1 i US 5

6 PURCHASING POWER PARITY THEORY PPP requires ha he inflaion rae differenial beween wo counries be equal o he change in he foreign exchange rae. F S / US / US 1 1 * Inflaion rae differenial Therefore, he forward exchange rae for one period forward is: / US F S / US 1 1 * 6

7 : VALUING IN FOREING AN OMESTIC CURRENCY Valuaion in foreign currency (i.e. dollars): V US FCF (1 WACC US US 1 ) Valuaion in domesic currency (i.e. pesos): V FCF (1 WACC 1 ) For valuing he company in domesic currency, we have o perform wo adjusmen firs, one in he cos of capial and he oher in he nominal long-erm growh rae 7

8 EXPECTE (IMPLICIT) OMESTIC INFLATION RATE IRP, coupled wih PPP and he expecaions heory of forward exchange raes, implies he inernaional Fisher effec. To be consisen, boh heories should be predicing he same forward exchange rae: F / US S / US 1 i 1 i US S / US 1 1 * Since he inflaion rae in developed counries is around 2%, we can assume i will remain consan along he forecas period. Once he forward exchange rae was obained using he IRP and we know he spo exchange rae and he inernaional inflaion rae, we can obain he implied domesic inflaion rae: F S / US / US (1 ) 1 * 8

9 AJUSTMENT 1: COST OF CAPITAL IN OMESTIC CURRENCY The inflaion rae observed in emerging counries is higher compared o he inflaion rae observed in developed counries US (1 ) ( 1WACC ) (1 WACC ) * (1 ) Inflaion rae differenial * = period domesic inflaion rae = period inernaional inflaion rae 9

10 EXERCISES IRP saes ha he change in he exchange rae is equal o he differenial beween he..exchange rae and he.exchange rae. Equivalenly, i implies ha he forward exchange rae is equal o he exchange rae muliplied by he ineres rae.. PPP saes ha he change in he exchange rae is equal o he differenial beween he..inflaion rae and he.inflaion rae. Equivalenly, i implies ha he forward exchange rae is equal o he exchange rae muliplied by he.. rae.. More imporan, if he forward exchange rae was esimaed using he IRP, hen he domesic inflaion rae mus be equal o he rae differenial muliplied by (1+ )-1 10

11 EXERCISES Using he following daa, calculae he company value assuming perpeuiies. Esimae firs he value in dollars and hen in domesic currency (pesos). FCF 100 ER 0 10 ER 1 10,19 WACC US 10% Yield emerg. Bond 7% Yield emerg. Bond US 5% Inernac. Inflaion rae 2% 11

12 STEP 1: VALUING IN FOREIGN CURRENCY Sep 1: once he forward Exchange rae was foreased, he cash flow is expressed in dollars and he company value is calculaed discouning i wih he WACC expressed in dollars: 12

13 STEP 2: VALUING IN OMESTIC CURRENCY For valuing in domesic currency we need o express he WACC in domesic currency. I will be equal o he WACC in dollars adjused by he inflaion rae differenial. To obain he inflaion rae differenial, we need o esimae he domesic inflaion rae (he inflaion rae in he emerging counry). We will use he PPP heory o perform his esimaion. 13

14 STEP 2: VALUING IN OMESTIC CURRENCY Once he forward Exchange rae was obained using he IRP, we can exrac he domesic (implici) inflaion rae in he emerging counry so boh heory hold (noice ha we assumed an inernaional inflaion rae of 2%) 10,19 10 (1 EMERG (1 0,02) ) EMERG 3,94% 14

15 STEP 2: VALUING IN OMESTIC CURRENCY Then he WACC in dollars is adjused by he inflaion rae differenial o obain he WACC in domesic currency. Finally, he FC is discouned wih he WACC o obain he company value in domesic currency. We have demonsraed ha V /ER 0 =V US 15

16 AJUSTMENT 2: LONG-TERM GROWTH RATE IN OMESTIC CURRENCY The same adjusmen have o be performed in he domesic long-erm growh rae g, in order o calculae he erminal value for a company ha operaes in an emerging or foreign marke. TV US FCFT WACC US (1 US T g g * ) * This is equal o he nominal long-erm growh rae observed in developed counries adjused by he inflaion rae differenial: g g * (1 T ) * (1 ) T Inflaion rae differenial g * = nominal long-erm growh rae in he developed counry, g = nominal long-erm growh rae in he emerging counry, T = las forecas period domesic inflaion rae, TV FCF T WACC (1 T g g ) * T = las forecas period inernaional inflaion rae. 16

17 EXERCISE You have o demonsrae he equivalence of valuing in foreign and domesic currency of runk Counry Corp using he following daa: aa aa cos of capial Spo exchange rae 10 rf 3% Yield 7% MRP 6% Yield US 4% Bea 1,20 Inernac. Infl. Rae 2% kd 9% LT growh rae g* 4,00% /V 25% 35% CRP 1% Company value in US$ Yr 0 Yr 1 Yr 2 Yr 3 FCF Forward exchange rae 10,29 10,59 10,89 FCF US 1,46 1,61 1,65 Terminal value 29,32 FCF US + TV 1,46 1,61 30,97 17

18 SOLUTION 18

19 FORECASTING THE EXCHANGE RATE WITH THE YIEL CURVES Previous examples assumed a fla yield curve. A yield curve is ransiional; he mos common form is upward sloping. One way o forecas he Exchange rae is hrough he yield curves for bonds issued by he same issuer expressed in domesic and foreign currency. 19

20 A HYPOTHETICAL EXAMPLE Foreign invesor is a company ha has operaions in several counries and is considering an acquisiion in México. The senior managemen is required o creae a consisen se of macroeconomic assumpions regarding he exchange rae, he domesic inflaion rae, he ineres raes, and he GP growh. The arge acquisiion s FCF is expeced o grow a a rae of 3% per year plus he domesic inflaion rae. Beyond his period, FCF is expeced o grow a a rae of 2% per year plus he domesic inflaion rae. A Terminal Value in foreign and domesic currency is esimaed using Equaions 10 and 11, he WACC expressed in dollars is esimaed o be 15%, and he spo exchange rae is S /US =

21 FORECASTING THE EXCHANGE RATE USING MARKET BONS YIELS In emerging markes, he forward exchange raes are no liquid or are no available beyond 12/18 monhs. To obain he company fair value in dollars, analyss need o forecas he forward exchange rae for a longer horizon. 10% 8% 6% 4% 2% 0% -2% Yield y = 0,0069ln(x) + 0,0542 R² = 0,7988 y = 0,0195ln(x) + 0,0025 R² = 0, To fill he gap, we can use he daa of marke bond yields in an emerging counry and assuming he IRP holds, forecas he forward exchange rae for he explici forecas period. -4% -6% US Modified duraion omesic currency Emerging marke bonds issued in local currency generally pay a premium in comparison o bonds issued in dollars. Since he issuer and he jurisdicion are he same and differ solely in he currency, he yield spread reflecs he marke s opinion abou he forward exchange rae. 21

22 FORECASTING THE EXCHANGE RATE USING MARKET BONS YIELS Since he marke requires a currency premium for he devaluaion risk, he yield spread reflecs he marke s opinion abou he expeced exchange rae. Analyss can easily obain he required reurns for a specific year using he yield curve equaions. For example, o calculae he required reurn in domesic currency and dollars for one year from now: i 1 = 0, ,0069 ln 1 = 5,42% i 1 US = 0, ,0195 ln 1 = 0,25% To obain he expeced yields for subsequen years, analyss only have o change he year number in he equaion: i 1 = 0, ,0069 ln 3 = 6,18% i 1 US = 0, ,0195 ln 3 = 2,39% 22

23 FORECASTING THE EXCHANGE RATE USING MARKET BONS YIELS To forecas he forward exchange rae for a specific year, analyss can exrapolae wha some marke paricipans refer o as he marke s consensus of forward ineres raes. Given he wo-year spo rae, here could be a rae on a one-year insrumen one year from now ha will make he invesor indifferen beween wo alernaives: f (1 i2 (1 i ) ) US 2 US 1 US 1 For example, o forecas he expeced exchange rae for wo years from now: US US / US / US (1 i1 )(1 f1 ) F2 S (1 i )(1 f ) The forward exchange rae is esimaed using IRP raher han PPP. This is because one can observe forward ineres raes in he marke, bu one canno direcly observe he expeced inflaion raes. 23

24 AJUSTMENT 3: COST OF CAPITAL AN THE SLOPE OF THE YIEL CURVE Equaions 5 and 6 assume a fla yield curve. In a valuaion, i is common ha praciioners consider a consan cos of capial along he invesmen horizon. However, he common yield curve is upward sloping (he invered yield curve generally means he expecaions of a downurn and he fla yield curve is ransiional). If he ineres raes change wih mauriy, he cos of capial mus be calculaed for each period. The WACC expressed in dollars for he -period will be equal o he WACC expressed in dollars for he -1 period plus he change in he ineres rae: WACC US WACC US 1 US US ( i i 1 ) 24

25 VALUING IN OMESTIC OF FOREING CURRENCY: THE EQUIVALENCE Yr 0 Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 Yr 7 Yr 8 Yr 9 Yr 10 FCF 100,00 109,50 119,30 129,50 140,19 151,42 163,23 175,69 188,82 202,67 Terminal Value 1.565,42 FCF 100,00 109,50 119,30 129,50 140,19 151,42 163,23 175,69 188, ,09 FCF US 8,11 8,52 8,96 9,41 9,89 10,39 10,91 11,46 12,04 12,65 Terminal Value US 97,73 FCF US 8,11 8,52 8,96 9,41 9,89 10,39 10,91 11,46 12,04 110,38 F /US 11,72 12,32 12,85 13,32 13,76 14,18 14,58 14,96 15,33 15,68 16,02 i 5,42% 5,90% 6,18% 6,38% 6,53% 6,66% 6,76% 6,85% 6,94% 7,01% i US 0,25% 1,60% 2,39% 2,95% 3,39% 3,74% 4,04% 4,30% 4,53% 4,74% 7,26% 6,31% 5,77% 5,39% 5,10% 4,86% 4,66% 4,49% 4,34% 4,21% * 2,00% 2,00% 2,00% 2,00% 2,00% 2,00% 2,00% 2,00% 2,00% 2,00% isc. facor US 0,87 0,75 0,65 0,56 0,48 0,42 0,36 0,32 0,27 0,24 PV Cash Flow US 70,73 7,06 6,37 5,78 5,26 4,78 4,36 3,97 3,62 3,30 26,24 isc. facor 0,83 0,68 0,57 0,48 0,40 0,34 0,28 0,24 0,20 0,17 PV Cash Flow 828,95 82,69 74,67 67,75 61,59 56,06 51,05 46,52 42,40 38,66 307,57 Real exchange rae 11,72 11,72 11,72 11,72 11,72 11,72 11,72 11,72 11,72 11,72 11,72 US V 828,95 11,72 70,73 25

26 REAL EXCHANGE RATE If he PPP holds and boh heories predic he same exchange rae, i implies ha he RER remains consan along he projecion. To illusrae for one single year: RER / US 0 F / US 1 1 * For praciioners, he esimaed value of he RER is exremely imporan a he momen o decide an invesmen, in order o avoid an undervaluaion or an overvaluaion 26

27 CONCLUSIONS Valuaion in foreign currency or in domesic currency yields idenical values when he simulaneous fulfillmen of boh IRP and PPP is assumed. A simple fac: an asse canno be sold for more han one price in he marke. One way o forecas he expeced exchange rae is o adjus he spo rae by he yield spread observed in marke sovereign bonds for differen currencies. While our approach is essenially a suggesion for valuaion in emerging markes, i can also be used by mulinaionals which have businesses in developed counries. 27