chapter 7 cross-border capital budgeting

Kirt C. Butler, Multinational Finance, South-Western College Publishing, 2e 7-1

Chapter 7Chapter 7Cross-Border Capital BudgetingCross-Border Capital Budgeting

Table of contents

7.1 The Algebra of Cross-Border Investment Analysis

7.2 An Example: Wendy’s Restaurant in Neverland

7.3 The Parent vs Local Perspective on Project Valuation

7.4 Special Circumstances in Cross-Border Investments

7.5 Summary


““Domestic” NPV calculationsDomestic” NPV calculations

NPV0 = t E[CFt ] / (1+i )t

1. Estimate expected future cash flows E[CFt]– Include only incremental cash flows

– Include all opportunity costs

2. Identify a risk-adjusted discount rate– Discount nominal (real) CFs at nominal (real) discount rates

– Discount equity (debt) CFs at equity (debt) discount rates

– Discount CFs to debt and equity at the WACC

– Discount cash flows in a particular currency at a discount rate in that currency

3. Find NPV0


Cross-border capital budgetingCross-border capital budgeting

Foreign projects generate foreign currency cash flows.

Recipe #1: Discount in the foreign currency and convert the foreign currency NPV to a domestic currency value at the spot exchange rate.

Recipe #2: Convert expected future cash flows into domestic currency cash flows at expected future exchange rates and then discount in the domestic currency.


Recipe #1: Discount in the foreign currencyRecipe #1: Discount in the foreign currency

NPV0d = S0

d/f [NPV0f ] = S0

d/f [t E[CFtf ] / (1+if )t ]

1. Estimate CFtf

2. Identify if

3. Find NPV0d

a. Calculate NPV0f by discounting E[CFt

f] at if

b. Convert NPV0f to NPV0

d at S0d/f

CF1f CF2

f

ifNPV0f

NPV0d = S0

d/f NPV0f


Recipe #2: Discount in the domestic currencyRecipe #2: Discount in the domestic currency

NPV0d = t E[CFt

d] / (1+id )t = t Ftd/f E[CFt

f] / (1+id )t

1. Estimate CFtd a. Estimate CFt

f

b. Estimate Std/f = Ft

d/f

c. Convert CFtf to CFt

d at Ftd/f

2 Identify id

3. Calculate NPV0d

E[CF1f] E[CF2

f]

E[CFtd] . . . = Ft

d/f E[CFtf]

idNPV0d


Equivalence of the two recipesEquivalence of the two recipes

NPV0d = t E[CFt

d ] / (1+id )t

plus E[CFtd ] = E[CFt

f ] E[Std/f ] = E[CFt

f ] Ftd/f

yields NPV0d = t Ft

d/f E[CFtf ] / (1+id )t

Rule #2: Convert expected foreign currency cash flows to domestic cash flows and discount in the domestic currency.

plus (1+id )t = (1+if )t (Ftd/f / S0

d/f )

yields NPV0d = t Ft

d/f E[CFtf ]/ {(1+if )t (Ft

d/f / S0d/f )}

= (S0d/f )t E[CFt

f ] / {(1+if )t

= (S0d/f )(NPV0

f)

Rule #1: Discount in the foreign currency and then convert into domestic currency at the spot exchange rate.


An example: Wendy in NeverlandAn example: Wendy in Neverland

U.S. Neverland

Nominal government T-bill rate iF$ = 10% iF

Cr = 37.5%

Real required return on T-bills rF$ = 1% rF

Cr = 1%

Expected inflation p$ 8.91% pCr 36.14%

Nominal risk-adjusted required return i$ = 20% iCr = 50%

Real risk-adjusted required return r$ 10.18% rCr 10.18%

Spot exchange rate S0Cr/$ = Cr4/$


Suppose the int’l parity conditions holdSuppose the int’l parity conditions hold

If the international parity conditions hold, then

(1+iCr) = (1+pCr)(1+rCr) iFCr = (1.3614)(1.0100) 1 = 37.5%

iWACCCr(1.3614)(1.1018) 1= 50.0%

(1+i$) = (1+p$)(1+r$) iF$(1.0891)(1.0100) 1 = 10.0%

iWACC$(1.0891)(1.1018) 1 = 20.0%

F1Cr/$/S0

Cr/$ = (1+pCr) / (1+p$) = (1.3614) / (1.0891)

= (1+iCr) / (1+i$) = (1.50) / (1.20)

= (1+iFCr) / (1+iF

$) = (1.3750) / (1.1000)

= E[S1Cr/$] / S0

Cr/$ = 1.25

the dollar should sell at a 25% forward premium.


Wendy’s expected future spot exchange ratesWendy’s expected future spot exchange rates

Expected future spot exchange rates should reflect the 25% difference in inflation (or nominal interest rates)

Time Date E[S1Cr/$]

0 12/31/97 Cr4.0000/$

1 12/31/98 Cr5.0000/$

2 12/31/99 Cr6.2500/$

3 12/31/00 Cr7.8125/$

4 12/31/01 Cr9.7656/$


Details of the Neverland projectDetails of the Neverland project

Investment of $10,000 (Cr40,000) for the ship at time t=0 Investment of $6,000 (Cr24,000) for inventory at time t=0 Expected revenues of Cr30,000, Cr60,000, Cr90,000, and

Cr60,000 in years 1 through 4 Variable operating costs are 20% of sales Fixed operating costs are Cr2,000 at the end of the first year and

increase at the rate of inflation thereafter The ship is owned by the foreign affiliate and depreciated

straight-line to a zero salvage value Inventory is sold at the end of the project for Cr24,000 in real

terms The ship is expected to retain its Cr40,000 real value Income and capital gains taxes are 50% in each country All cash flows occur at the end of the year


Wendy’s investment/disinvestment cash flowsWendy’s investment/disinvestment cash flowsWendy’s investment/disinvestment cash flowsWendy’s investment/disinvestment cash flows

End-of-year CFs in crocs

t=0 t=1 t=2 t=3 t=4

Purchase ship Cr40,000

Purchase inventory 24,000

Sale of ship Cr137,400

Tax on sale of ship 68,700

Sale of inventory 82,440

Tax on sale of inventory 29,220


Wendy’s operating cash flowsWendy’s operating cash flowsWendy’s operating cash flowsWendy’s operating cash flows

t=0 t=1 t=2 t=3 t=4

Revenues Cr30,000 Cr60,000Cr90,000Cr60,000

-Variable costs -6,000 -12,000 -18,000 -12,000

-Fixed cost -2,000 -2,723 -3,707 -5,046

-Depreciation -10,000 -10,000 -10,000 -10,000

Taxable income 12,000 35,277 58,293 32,954

- Taxes - 6,000 -17,639 -29,147 -16,477

Net income 6,000 17,639 29,147 16,477

+Depreciation 10,000 10,000 10,000 10,000

NCF from operations 16,000 27,639 39,147 26,477

E[CFtCr] 64,000 16,000 27,639 39,147 148,397

NPV0Cr = Cr137 at iCr=50% or NPV0

$ = $34 at S0Cr/$ = Cr4/$


Discount in the domestic currencyDiscount in the domestic currencyDiscount in the domestic currencyDiscount in the domestic currency

t=0 t=1 t=2 t=3 t=4

E[CFtCr] Cr64,000 Cr16,000 Cr27,639 Cr39,147 Cr148,397

FtCr/$ Cr4.0000/$ Cr5.0000/$ Cr6.2500/$ Cr7.8125/$ Cr9.766/$

E[CFt$] $3,200 $4,422 $5,011 $15,196

$16,000

NPV0$ = $34 i$ = 20%


Valuation when the international parity Valuation when the international parity conditions do not holdconditions do not hold

NPVf < 0

NPVf > 0

NPVd < 0 NPVd > 0

Reject

Try to lock in thevalue NPVf in the foreign currency

Accept

Look for betterprojects in the foreign currency


Special circumstancesSpecial circumstances

VPROJECT WITH SIDE EFFECT

= VPROJECT WITHOUT SIDE EFFECT + VSIDE EFFECT

Blocked funds Subsidized financing Negative-NPV tie-in projects Expropriation risk Tax holidays


Blocked fundsBlocked fundsExample: ½ of cash flow blocked in each of the first 3 yearsExample: ½ of cash flow blocked in each of the first 3 years

Market rate Hook’s rate

(37½%) (0%)

20,797.08,000.0

26,127.013,819.5

26,914.019,573.5

Cr8,000 13,819.5 19,573.5

Cr20,657 73,838.0 41,393.0

Cr11,580

discounted at 37½% for four years

Opportunity cost of blocked funds = Cr20,657Cr11,580 = Cr9,077

VPROJECT W/ SIDE EFFECT = VPROJECT W/O SIDE EFFECT + VSIDE EFFECT

= Cr137Cr9,077

= Cr9,214 or $2,303.5 at Cr4/$


Subsidized financingSubsidized financingExample: a below-market-rate loan of Cr40,000 at 37.5%Example: a below-market-rate loan of Cr40,000 at 37.5%

Base Case: Suppose Wendy can borrow Cr40,000 at the prevailing croc corporate bond rate of 40%

(0.40)(Cr40,000) = Cr16,000 in annual interest

Alternative: Suppose Hook will loan Wendy Cr40,000 at the government borrowing rate of 37½%

(0.375)(Cr40,000) = Cr15,000 in annual interest

Net result: Cr1,000 in annual pre-tax interest savings

or Cr500 in annual after-tax interest savings

Valuing Wendy’s after-tax interest savings at the after-tax

cost of 40%(10.5) = 20%, this is worth Cr1,295 today.


Expropriation riskExpropriation riskExample: a 50% chance of losing the time t=4 cash flowExample: a 50% chance of losing the time t=4 cash flow

Alternative #1: Discounting at the croc required return iCr = 50%

E[loss from expropriation]

= [(0.5) [Cr148,397) / (1.50)4 ] / (Cr4.00/$)]

= $3,664 the Cr4.00/$ spot exchange rate

Alternative #2: Discounting at the dollar required return i$ = 20%

E[loss from expropriation]

= [ (0.5) [ (Cr148,397) / (Cr9.7656/$)] ] / (1.20)4

= $3,664 at the 10% U.S. discount rate

chapter 7 cross-border capital budgeting

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