Class 11

Applications:

International Finance

and

Real Options

Offshore Borrowing

Suppose you are an Australian wheat farmer and you want to borrow to expand your operations.

You face a rate of 12% in Australian Dollar-denominated loans.

A Swiss bank, however, will lend at 9% by way of Swiss Franc-denominated loans.

What should you do?

Offshore Borrowing

Suppose you intend to borrow 10 million AUD for 5 years. The spot rate is 0.8 AUD/CHF.

AUD loan:

CHF loan:

0 5

10 m AUD 10(1.12)5 m AUD

0 5

12.5 m CHF 12.5(1.09)5 m CHF

Offshore Borrowing

The question is whether 10(1.12)5 m AUD will be more than 12.5(1.09)5 m CHF.

This depends on the spot rate 5 years from now, which is uncertain.

Since most wheat farmers are better at growing wheat than forecasting foreign exchange rate movements, you decide to hedge this risk using the forward market.

Offshore Borrowing

Suppose the 5-year forward rate is 0.91632 AUD/CHF.

Paying back the 12.5(1.09)5 m CHF will require 12.5(1.09)5(0.91632) m AUD = 17.62 m AUD

But this is exactly what would have to be repaid under the AUD loan since 10(1.12)5 m AUD = 17.62 m AUD.

Hence nothing has been gained by borrowing offshore.

Covered Interest Rate Parity

This equivalence always holds and is known as covered interest rate parity:

F Sr

rTAUD CHF AUD CHF T

AUD T

TCHF T

/ /

0

1

1

c hc h

0 91632 0 8112

109

5

5. ..

.b gb g

Proof By Arbitrage

Suppose the forward rate is 0.80 AUD/CHF: Borrow 1.25 CHF and convert to 1.00 AUD. Invest for 5 years at 12% yielding

1.00(1.12)5=1.76 AUD in 5 years. Convert to 1.76/0.8=2.20 CHF. Repay CHF loan with 1.25(1.09)5=1.92 CHF. The remaining 2.20-1.92=0.28 is an arbitrage

profit.

Proof By Arbitrage

Suppose the forward rate is 1.00 AUD/CHF: Borrow 1.00 AUD and convert to 1.25 CHF. Invest for 5 years at 9% yielding 1.25(1.09)5=1.92

CHF in 5 years. Convert to 1.92(1.00)=1.92 AUD. Repay AUD loan with 1.00(1.12)5=1.76 AUD. The remaining 1.92-1.76=0.16 is an arbitrage

profit.

Real Options

Standard discounted cash flow or net present value analysis ignores real or strategic options available to the firm.

Discounting the expected cash flow ignores the flexibility that management may have to abandon the project if the cash flows appear likely to be negative.

The most common real option is the option to abandon the project as uncertainty is revealed.

The Abandonment Option

-50

-50

-50

Good

Bad

200

120

90

-100

0 1 2

Cash Flows

0.7

0.3

0.8

0.2

0.8

0.2

The Abandonment Option

Expected NPV:

E NPV T[ ].

. ( . . ) . ( . . )

.

.

5050

11

0 7 0 8 200 0 2 120 0 3 0 2 90 08 100

11

4 38

2

bg

bg

The Abandonment Option

Abandonment Option:

E NPV T[ ]. ( )

.

. ( . . ) . ( )

.

500 7 50

11

0 7 0 8 200 0 2 120 0 3 0

11

20

2

bg

bg

Types of Real Options

Input Mix/Process Flexibility Output Mix/Product Flexibility Abandonment/Termination Temporary Stop/Shutdown Intensity/Operating Scale Initiation/Deferment Sequencing

Natural Resource Investments

Your company has a two year lease to extract copper from a deposit. The deposit contains 8 million pounds of copper. A 1-year development phase costs $1.25 immediately. Extraction costs of 85 cents per pound would be paid to a contractor in advance. The rights to the copper would be sold at the spot price of copper one year from now. Percentage price changes for copper are N(0.07, 0.20). The current spot price is 95 cents. The discount rate for this kind of project (from the CAPM) is 10% and the riskless rate is 5%.

Standard Expected NPV Analysis

E NPVE S

[ ] .( [ ] . )

.

125

8 0 85

111

E S S eTT[ ] 0

E S e[ ] . ..1

0 070 95 11089

E NPV[ ] .( . . )

..

125

8 10189 0 85

110 022

Option Analysis

0 1

-1.25 Max[S1-0.85,0]

0.85 S1

Payoff

Option Analysis

C S d Xe drT N N( ) ( )1 2

d

SX

r T

T

d

f

1

2

1

2

0 5

0 950 85

0 05 0 5 0 20 1

0 20 10 906

FHGIKJ

FHGIKJ

ln .

ln..

. . ( . )

..

d i

c h

Option Analysis

d d T2 1 0 906 0 20 0 706 . . .

C e 0 85 0 906 0 85 0 706 01620 05 1. ( . ) . ( . ) .. ( )N N

Terminal Distribution

Distribution of Copper Price at Time 1

0.00

0.50

1.00

1.50

2.00

2.50

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

Copper Price

Pro

bab

ility

De

nsi

ty

Shutdown and Restart Options

{

}

C

O

Gold PriceP2P1

Present Value ofOpen Mine

Present Value of Closed Mine

PresentValue