14- 1
B40.2302 Class #9
 BM6 chapters 25.2-25.6, 26, 27
25: Leasing
 26: Risk management
 27: International risk management

 Based on slides created by Matthew Will
 Modified 11/07/2001 by Jeffrey Wurgler
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Leasing
Slides by
Matthew Will,
Jeffrey Wurgler
Irwin/McGraw Hill
Chapter
25.2-25.6
©The McGraw-Hill Companies, Inc., 2000
14- 3
Topics Covered
 Why Lease?
 Operating (Short-term) Leases
 Financial (Long-term) Leases
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Why Lease?
 Sensible (Non-tax) Reasons for Leasing

Short-term leases are convenient

Cancellation options are valuable

Maintenance may be provided

Standardization leads to low transaction costs
• (Relative to bond or stock issue)
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Why Lease?
 Sensible (Tax) Reasons for Leasing

Tax shields can be used
• Lessor owns asset, and so deducts its depreciation
• If lessor can make better use of tax shield than lessee, then lessor
should own equipment and pass on some tax benefits to lessee (in
form of lower lease payments)
• So direct tax gain to lessor, indirect gain to lessee

Reduces the alternative minimum tax (AMT)
• Corporate tax = max{regular tax, AMT}
• Leasing (as opposed to buying) reduces lessee’s AMT
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Why Lease?
 Dubious Reasons for Leasing

Leasing avoids internal capital expenditure
controls

Leasing preserves capital
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Why Lease?
 Dubious Reasons for Leasing (contd.)

Leases may be off-balance-sheet financing
• In Germany, all leases are off balance sheet
• In US, only operating leases are off balance sheet

Leasing affects book income
• Leasing reduces book income bec. lease payments are
expensed
• Buy-and-borrow alternative reduces book income
through both interest and depreciation
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Operating Leases
 Review: Suppose you decide to lease a
machine for one year
Q: What is the rental payment in a competitive
leasing industry?
A: The lessor’s equivalent annual cost (EAC)
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Operating Leases
Example: Calculate a competitive lease payment / EAC
Acme Limo has a client who will sign a lease for 7 years, with lease payments due
at the start of each year. The following table shows the NPV of the limo if Acme
purchases the new limo for $75,000 and leases it out for 7 years.
(amounts in 000s)
0
Initial cost
Maintenance, insurance, selling,
and administrative costs
Tax shield on costs
Depreciation tax shield
Total
PV @ 7% = - $98.15
Break even rent(level)
Tax
Break even rent after-tax
PV @ 7% = $98.15
Irwin/McGraw Hill
1
Year
3
2
4
5
6
-75
-12
-12
-12
-12
-12
-12
-12
4.2
0
-82.8
4.2
5.25
-2.55
4.2
8.4
0.6
4.2
5.04
-2.76
4.2
3.02
-4.78
4.2
3.02
-4.78
4.2
1.51
-6.29
26.18
-9.16
17.02
26.18
-9.16
17.02
26.18
-9.16
17.02
26.18
-9.16
17.02
26.18
-9.16
17.02
26.18
-9.16
17.02
26.18
-9.16
17.02
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14- 10
Operating Leases
 Bottom line for lessee: Operating lease or buy?
Buy if the lessee’s equivalent annual cost of ownership and
operation is less than the best available operating lease
rate
Otherwise lease
 Complication: If operating lease includes option to
cancel/abandon, need to factor that in
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Financial Leases
Example - cont
Greymare Bus Lines is considering a lease. Your operating manager
wants to buy a new bus for $100,000. The bus has an 8 year life. An
alternative is to lease the bus for 8 years at $16,900 per year, but
Greymare still assumes all operating and maintenance costs.
Should Greymare buy or lease the bus?
Cash flow consequences of the financial lease contract:
•Greymare saves the $100,000 cost of the bus.
•Loss of depreciation benefit of owning the bus.
•$16,900 lease payment is due at the start of each year.
•Lease payments are tax deductible.
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Financial Leases
Cash flow consequences of the financial lease contract
(amounts in 000s)
0
Cost of new bus
100.00
Lost Depr tax shield
Lease payment
(16.90)
Tax shield of lease pmt.
5.92
Net cash flow of lease
89.02
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1
2
(7.00)
(16.90)
5.92
(17.98)
(11.20)
(16.90)
5.92
(22.18)
Year
3
(6.72)
(16.90)
5.92
(17.70)
4
5
6
7
(4.03)
(16.90)
5.92
(15.01)
(4.03)
(16.90)
5.92
(15.01)
(2.02)
(16.90)
5.92
(13.00)
(16.90)
5.92
(10.98)
©The McGraw-Hill Companies, Inc., 2000
14- 13
Financial Leases
How to discount CFs?
Since lessor is essentially lending money to
lessee, appropriate rate is the equivalent
lending/borrowing rate
• Lender pays tax on interest it receives: net return is after-tax
interest rate
• Borrower deducts interest from taxable income: net cost is aftertax interest rate
• Thus, after-tax interest rate is effective rate at which company
can transfer debt-equivalent cash flows across time
• Suppose Greymare can borrow at 10%. Then the lease payments
should be discounted at (1-.35)*.10 =.065.
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Financial Leases
Example – contd.
Greymare Bus Lines can borrow at 10%, thus the value of the lease
should be discounted at 6.5% or .10 x (1-.35). The result will tell us if
Greymare should lease or buy the bus.
17.99 22.19
17.71
15.02
NPV lease  89.02 2
3
4
1.065 1.065 1.065 1.065
15.02
13.00
10.98
5
6
1.065 1.065 1.0657
 .70 or - $700
 Buy, don’t lease
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Financial Leases
Example – Equivalent loan cash flows
Another way to think about where the lease value comes from (or goes) is
to imagine a loan that generates exactly the same year 1 - 7 cash outflows
as the lease.
(amounts in 000s)
0
Amount borrowed
at year end
Interest paid @ 10%
Tax shield @ 35%
Interest paid after tax
Principal repaid
Net cash flow of
equivalent loan
1
2
Year
3
4
5
6
7
89.72
77.56
-8.97
3.14
-5.83
-12.15
60.42
-7.76
2.71
-5.04
-17.14
46.64
-6.04
2.11
-3.93
-13.78
34.66
-4.66
1.63
-3.03
-11.99
21.89
-3.47
1.21
-2.25
-12.76
10.31
-2.19
0.77
-1.42
-11.58
0.00
-1.03
0.36
-0.67
-10.31
89.72
-17.99
-22.19
-17.71
-15.02
-15.02
-13.00
-10.98
This costs same, but brings in 89.72 in year 0 (vs. 89.02 in the lease).
Thus, borrowing-and-buying is 89.72-89.02=0.70=$700 better than lease.
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Financial Leases
 Bottom line for lessee: Financial lease or buyand-borrow?
Buy-and-borrow if can devise a borrowing plan that
gives same cash flow as lease in every future
period, but higher immediate cash flow
(equivalently, buy-and-borrow if incremental
lease cash flows are NPV<0)
Otherwise lease
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Leases in APV framework
• Can think of leases as financing that may have side effects.
• Thus, the APV of a project financed by a lease:
APV  NPV of project  NPV of lease
• This is consistent with all the previous examples.
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Managing Risk
Slides by
Matthew Will,
Jeffrey Wurgler
Irwin/McGraw Hill
Chapter 26
©The McGraw-Hill Companies, Inc., 2000
14- 19
Topics Covered
 Insurance
 Futures contracts
 Forward contracts
 Swaps
 How to set up a hedge
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Insurance
 Most businesses insure against fire, theft,
environmental liability, vehicle accidents, etc.
 Insurance transfers risk from company to insurer
 Insurers pool risks
The claims on any individual policy are very risky…
 … but the claims on a large portfolio of policies may be
quite predictable
 This gives insurers a risk-bearing advantage
 Of course, insurers cannot diversify away macro risks

• In same way that investors can’t diversify away systematic risk
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Insurance
Example
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm
over the course of the next year. What is the “fair
price” of insurance?
Answer:
There is no systematic risk; it’s all due to the weather
Therefore no systematic risk premium required
The expected loss per year is
= (1/10,000)*$1 billion = $100,000 = “fair price”
But for several reasons we’d expect a higher price …
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Insurance
 Why would an insurance company probably
not offer a policy on this oil platform for
$100,000/yr?
Administrative costs
 Adverse selection
 Moral hazard

 If these costs are large, there may be cheaper
ways to protect against risk
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Insurance: British Petroleum
 During the 1980s BP paid out $115m/year in
insurance, recovered $25m/year in claims
 BP has decided to cut down insurance
BP felt it was better-placed to assess risk
 And insurance was not competitively priced

 So now BP assumes more risk than when it insured
BP guesses a big loss of $500m happens every 30 years
 Even so, this is <1% of BP market equity !
 BP can afford not to insure against these risks

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Hedging
Hedging
Taking on one risk to offset another
Some basic tools for hedging
Futures
 Forwards
 Swaps

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Futures
 Futures contract - A contract between two parties for the
delivery of an asset, at a negotiated price, on a set future date
 Example:




Wheat farmer expects to have 100,000 bushels of wheat next Sept.
He’s worried that price may decline in the meantime
To hedge this risk, he can sell 100,000 bushels of Sept. wheat futures
at a price that is set today
Bottom line -- perfect hedge
• If price rises, value of his wheat goes up but futures contract value falls
• If price falls, value of his wheat falls but futures contract value rises
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Futures
Futures are standardized contracts,
traded on organized futures exchanges
SUGAR
Commodity Futures
-Sugar -Corn -OJ -Lumber
-Wheat -Soybeans -Pork bellies
-Oil -Copper -Silver -...
Financial Futures
-Tbills -Japanese govt. bonds
-S&P 500 -DJIA index -...
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Futures
 When you buy a financial future, you end up with the same
security that you would have if you bought in the “spot
market” (i.e. on-the-spot today)
 Except:


You don’t pay up front, so you earn interest on purchase price
You miss out on any dividend or interest in interim
 Therefore for a financial future:
Futures price/(1+rf)t
= Spot price – PV(foregone interest or dividends)
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Futures
Futures price/(1+rf)t
= Spot price – PV(foregone interest or dividends)
Example: Stock index futures
Q: Suppose 6-month stock index futures trade at 1,235
when index is at 1,212. 6-month interest rate is 5% and
average dividend yield of stocks in index is 1.2%/year.
Are these #s consistent?
A: Yes:
Futures price/(1+rf)t = 1,235/(1.05)1/2 = 1,205
Spot price – PV(foregone interest or dividends)
= 1,212 – 1,212*(1/2)*(.012)/(1.05)1/2 = 1,205
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Futures
 When you buy a commodities future, you end up with the same
commodity that you would have if you bought in the “spot
market”
 Except:



You don’t pay up front, so you earn interest on purchase price
You don’t have to store the commodity in the interim; saves on storage
costs
You don’t get a “convenience yield” – the value of having the real thing
 So for a commodities future:
Futures price/(1+rf)t
= Spot price + PV(storage costs) – PV(convenience yield)
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Forwards
 Futures contracts are standardized, exchange
traded
 Forward contracts are tailor-made futures
contracts, not exchange traded
Main forward market is in foreign currency
 Also forward interest-rate contracts

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Forwards
Example: Lock in a rate today on a loan tomorrow
(“a homemade forward loan”)
 Suppose you borrow $90.91 for one year at 10%, and you lend $90.91 for two
years at 12%
 These are interest rates today, i.e. spot interest rates
 Net cash flow
 Year 0: 90.91 – 90.91 = 0
 Year 1: -90.91*1.10 = -100
 Year 2: 90.91*1.12*1.12 = 114.04
 So paid out 100 at year 1, take in 114.04 at year 2, essentially you made a
“forward loan” at locked-in interest rate of
 Fwd. rate = (1+r2)2/(1+ r1) – 1 = (1.12)2/(1.1) – 1 = .1404
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Swaps
Swap contract - An agreement between two parties
(“counterparties”) lend to each other on different
terms, e.g. in different currencies, or one at fixed rate
and the other at a floating rate
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Swaps
Example: Currency swap
USA Inc. wants to borrow euros to finance European
operations, but it gets better rates in US
So it issues US debt (say $10M of 8%, 5-year notes)
 And contracts with a bank to swap its future dollar
liability for euros
 Combined effect: convert an 8% dollar loan into a 5.9%
euro loan (see next page)

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Swaps
Net cash flow to USA Inc. after the currency swap
Year 0
Dollars
Years 1-4
Euros
Dollars
Year 5
Euros
-.8
Dollars
Euros
Dollar loan
+10
-10.8
Swap dollars for
euros
-10
+8.5
+.8
-.5
+10.8
-9.0
Net cash flow
0
+8.5
0
-.5
0
-9.0
Bottom line: currency swap turned dollar debt into euro debt
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Swaps
Example: Fixed-to-floating interest rate swap
Bancorp has made a 5-year, $50m loan at a fixed rate of 8%;
annual interest payments are $4m





Bank wants to swap the $4m, 5-year annuity (the fixed interest
payments) into a floating rate annuity
Bank has ability to borrow at 6% for 5 years. So $4m interest annuity
could support a fixed-rate loan of 4/.06 = $66.67m.
Bank can construct “homemade swap” by borrowing $66.67m at 6%
for 5 years, then simultaneously lend this amount at LIBOR (a
floating rate)
Bottom line: bank’s fixed rate interest stream has been converted into
a floating-rate stream
(Easier way to do all this: Bank could just call a swap dealer)
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Setting up a hedge
 In our futures examples, firm has hedged by buying one asset and selling
an equal amount of another
 In practice, the appropriate “hedge ratio” may not be 1.0

The asset to be hedged may not move 1-to-1 with the available hedge contract
 Suppose you own A and you want to hedge by making an offsetting sale
of B. If percentage changes in value of A and B are related as follows:
Expected change in A = a +
 *(change in B)
 Then delta  is the hedge ratio – the # of units of B that should be sold
to hedge each unit of A
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Setting up a hedge
 You can calculate deltas by brute force, or you can use
finance theory to set up a hedge
Example: Suppose a leasing company has a lease contract to
receive a fixed $1m for 5 years.




If interest rates go up (down), the value of the lease payments go
down (up)
The company can hedge this interest rate risk by financing the leased
asset with a package of debt that has exactly the same duration as
the lease payments
So if interest rates change, the lease payments’ value changes, but the
debt obligations change by an equal amount
We say the company is immunized against interest rate risk
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©The McGraw-Hill Companies, Inc., 2000
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Managing International Risk
Slides by
Matthew Will,
Jeffrey Wurgler
Irwin/McGraw Hill
Chapter 27
©The McGraw-Hill Companies, Inc., 2000
14- 39
Topics Covered
 Foreign Exchange Markets
 Some Basic Relationships
 Hedging Currency Risk
 International Capital Budgeting
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Foreign Exchange Markets
Exchange Rate - Amount of one currency needed
to purchase one unit of another.
Spot Exchange Rate – Price of currency for
immediate delivery.
Forward Exchange Rate – Price for future
delivery.
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Foreign Exchange Markets
Example - The yen spot price is 112.645 yen per dollar and the
3 month forward rate is 111.300 yen per dollar. What is the
forward premium, expressed as an annual rate?
Spot Price - Forward Price
= Premium or (-Discount )
Forward Price
112.645 - 111.300
4
x 100 = 4.8%
111.300
So yen trades at a “4.8% forward premium relative to dollar”
(could also say dollar sells at a 4.8% forward discount)
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Exchange Rate Relationships
 How are these various quantities related?
(i = inflation, f=forward rate, s=spot rate, r=interest rate)
1 + rforeign
1 + r$
E(1 + i$ )
?
?
f foreign/$
E(sforeign/$ )
sforeign/$
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?
E(1 + iforeign )
?
sforeign/$
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Exchange Rate Relationships
 In simplest world (people are risk-neutral and face no
transaction costs for international trade), they are all equal (!)
1 + rforeign
1 + r$
E(1 + i$ )
=
=
f foreign/$
E(sforeign/$ )
sforeign/$
Irwin/McGraw Hill
=
E(1 + iforeign )
=
sforeign/$
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14- 44
Exchange Rate Relationships
Leg #1) “Interest Rate Parity Theory” links interest
rates and exchange rates
1 + rforeign
1 + r$
=
f foreign/$
sforeign/$
 It says that the ratio between the interest rates in two
different countries is equal to the ratio of the forward
and spot exchange rates.
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Exchange Rate Relationships
Interest Rate Parity Example - You have $1,000,000
to invest for one year. You can buy a 1- year Japanese
bond (in yen) @ 0.25 % or a 1-year US bond (in
dollars) @ 5%.
The spot exchange rate is 112.645 yen:$1.
The 1-year forward exchange rate is 107.495 yen:$1
Which bond will you prefer?
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Exchange Rate Relationships
Interest Rate Parity Example - You have $1,000,000 to invest for one year.
You can buy a 1- year Japanese bond (in yen) @ 0.25 % or a 1-year US bond
(in dollars) @ 5%. The spot exchange rate is 112.645 yen:$1. The 1-year
forward exchange rate is 107.495 yen:$1. Which bond to prefer?
Next year’s payoff to dollar bond = $1,000,000 x 1.05 = $1,050,000
Next year’s payoff to Yen bond = $1,000,000 x 112.645 x 1.0025
= 112,927,000 yen
= 112,927,000/107.495 = $1,050,000
In other words, you are indifferent only if the interest rate
differential (1.0025)/(1.05) equals the difference between the
forward and spot exchange rates (107.495/112.645), as it
does here. (If this “interest rate parity” doesn’t hold, you’d
have an arbitrage opportunity. Hence, it must hold.)
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Exchange Rate Relationships
Leg #2) “Expectations Theory of Forward
Rates” links forward rates to expected spot
rates
E(sforeign/$ )
f foreign/$

sforeign/$
sforeign/$
 It says that in risk-neutral world, the expected future
spot exchange rate equals the forward rate
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Exchange Rate Relationships
Expectations theory logic
Suppose one-year forward rate on yen is 107.495
But that traders expect the future spot rate to be 120.
 Then no trader would be willing to buy yen forward,
since would get more yen by waiting and buying spot.
 Thus the forward rate will have to rise until the two rates
are equal
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Exchange Rate Relationships
Leg #3) “Purchasing Power Parity (PPP)”
implies that
E(sforeign/$ )
E(1 + iforeign )

E(1 + i$ )
sforeign/$
 And so the expected difference in inflation
rates equals the expected change in spot rates
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Exchange Rate Relationships
PPP intuition
If $1 buys a McDonald’s hamburger in the USA, it also buys (after
currency conversion) a hamburger in Japan
So spot exchange rates should be set such that $1 has the same
“purchasing power” around the world – else, there would be
import/export arbitrage – buy goods where $1 buys a lot, sell them
where $1 doesn’t buy much.
And if this relationship is to hold tomorrow as well, then the
expected change in the spot rate must reflect relative inflation.
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Exchange Rate Relationships
Leg #4) “International Fisher Effect” relates
relative interest rates to inflation rates
1 + rforeign
1 + r$
=
E(1 + iforeign )
E(1 + i$ )
 Says that expected inflation accounts for
differences in current interest rates, i.e. real
interest rates are the same across countries
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Exchange Rate Relationships
Example: International Fisher effect
Claims that the real interest rate in each country is about equal.
Suppose Japan and US, interest rates as before, expected
deflation in Japan is 2.5%, inflation in US is 2%. Then real
interest rates are about equal, Intl. Fisher effect holds.
1 + rforeign
1.0025
rforeign ( real ) 
=
= .028
E(1 + iforeign )
.975
1 + r$
1.05
r $( real ) 
=
= .029
E(1 + i$ ) 1.02
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Hedging Currency Risk
Outland Steel: Current situation

Has profitable export business

Contracts involve substantial payment delays

Company invoices in $, so it is naturally protected against
exchange rates

But wonders if it’s losing sales to firms that are willing to
accept foreign currencies…
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Hedging Currency Risk
Outland Steel: Proposal #1

Accept foreign currency payments…
• But if value of that currency declines before payment is made,
company may suffer a big loss in dollar terms

… and hedge by selling the currency forward
• If contract is to receive X yen next year, then sell X yen forward
today. Lock in dollar rate today.

Cost of this “insurance” is the difference between the
forward rate and the expected spot rate next year
• Cost =0 if these are equal, as in expectations theory (“leg #2”)
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Hedging Currency Risk
Outland Steel: Proposal #2


Accept foreign currency payments…
… and hedge by borrowing foreign currency against
foreign receivables, sell the currency spot, invest dollar
proceeds in the US
• Interest rate parity theory (“leg #1”) says that the difference
between selling forward and selling spot equals the difference
between foreign interest that you pay, and dollar interest you
receive

This should be equally effective as proposal #1
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International Capital Budgeting
Equivalent Intl. Capital Budgeting Techniques
1) (Easy) Discount foreign CFs at foreign cost of capital.
(Can then convert this present value to $ using spot
exchange rate.)
2) (Hard) Convert to $ assuming all currency risk was hedged
(use forward exchange rates), and then discount with $ cost
of capital.
These techniques are equivalent (verify BM6 p. 806-807)
Thus, hedging allows you to separate the investment
decision from decision to take on currency risk
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