1

International Project Evaluation and Real Options

Global Financial Management

Campbell R. HarveyFuqua School of Business

Duke Universitycharvey@mail.duke.edu

http://www.duke.edu/~charvey

2

Overview

Topics in Capital Budgeting Investments in international project

» What are the cost of capital?» How do you assess risk and returns in foreign

currencies? Capital budgeting and stratetic decisions

» Decision trees and real options

3

Offshore Borrowing

Suppose you are an Australian wheat farmer and you want to borrow to expand your operations.» You intend to borrow 10 million AUD for 5 years. The spot

rate is 0.8 AUD/CHF.» 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?

» Borrow 10m AUD in Australia?– repay 10*(1.12)5 AUD in 5 years

» Borrow 12.5m CHF, and convert into AUDs?– repay 12.5*(1.09)5 CHF in 5 years

4

Offshore Borrowing

The question is whether 10(1.12)5 m AUD will be more than 12.5(1.09)5 m CHF. » Depends on the spot rate 5 years from now, which is uncertain.» Decide to hedge this risk using the forward market.

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!

» Why does this work?

5

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

0 91632 0 8112

109

5

5. ..

.

6

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.

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.

7

International Capital Budgeting

Arctis, a canadian manufacturer of heating equipment, considers building a plant in Japan. The plant would cost Yen1.3m to build and would produce cash flows of Yen200,000 for the next 7 years. Other data are:» Yen interest rate:2.9%» C$ interest rate: 8.75%» Spot rate: Yen/C$: 83.86» Assumption: the investment is risk free

How should you calculate the NPV?

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Two Ways of Calculating NPV

Method I

Step 1: Forecast cash flows in Yen

Step 2: Discount at interest rate for Yen; gives NPV in Yen

Step 3: Convert NPV in Yen into Canadian dollars at spot exchange rate, gives NPV in C$

Method II

Step 1: Forecast cash flows in Yen

Step 2: Convert cash flows into C$ using implied forward rate

Step 3: Discount C$ cash flows using the interest rate for C$, gives NPV in C$.

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Results for Two Methods

Method I: Present value = -Yen 49,230

Method II: Present value = -C$ 590 = -Yen (590*83.86)=-Yen49,230

Both methods yield the same result!» Why is this necessary?

Year 1996 1997 1998 1999 2000 2001 2002 2003Forward rate 83.86 79.35 75.08 71.04 67.22 63.61 60.18 56.95Method ICash flows (Yen) -1300 200 200 200 200 200 200 200Discount factor (Yen) 1.000 0.972 0.944 0.918 0.892 0.867 0.842 0.819PV(Yen) -1300.000 194.363 188.886 183.562 178.389 173.362 168.476 163.728Method IICash flows (C$) -15.502 2.520 2.664 2.815 2.975 3.144 3.323 3.512Discount factor (C$) 1.000 0.920 0.846 0.778 0.715 0.657 0.605 0.556PV(C$) -15.502 2.318 2.252 2.189 2.127 2.067 2.009 1.952

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Alternative Exchange Rate Forecast

Suppose the corporate treasurer argues that the true value of the investment is understated, because the market is too pessimistic about the Yen» Assume the Yen appreciates 2.5% p. a. faster than

anticipated by the market

» Now the PV with Method II becomes C$ 976 or Yen 81,840– Now the project looks profitable, should you take it?

Year 1996 1997 1998 1999 2000 2001 2002 2003Time 0 1 2 3 4 5 6 7Forward rate 83.86 79.35 75.08 71.04 67.22 63.61 60.18 56.95Method ICash flows (Yen) -1300 200 200 200 200 200 200 200Discount factor (Yen) 1.000 0.972 0.944 0.918 0.892 0.867 0.842 0.819PV(Yen) -1300.000 194.363 188.886 183.562 178.389 173.362 168.476 163.728Method IIForward rate 83.862 77.367 71.375 65.847 60.747 56.043 51.702 47.698Cash flows (C$) -15.502 2.585 2.802 3.037 3.292 3.569 3.868 4.193PV(C$) -15.502 2.377 2.369 2.362 2.354 2.346 2.339 2.331

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Capital Budgeting and Currency Speculation

Break down your project into two investments:

1. Borrow C$ 15.502 and convert them into Yen for Yen1.3m;– Zero-NPV project

2. Invest the proceeds into plant for heating equipment– Negative NPV (Yen -49,230).

Compare this with an alternative combination of two investments:

1. Borrow C$ 14.915 and convert them into Yen for Yen1.251m;

2. Invest the proceeds into a 7-year bond with repayment of 200.– Positive NPV of C$ 1,563 if optimistic treasurer is correct

Hence, investing in plant has two consequences:» Profit of C$ 1,563 on speculation on Yen» Loss of C$ 587 on plant» Net gain is 1,563-587=C$976

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SummaryInternational Capital Budgeting

There is no easy gain from offshore borrowing» Implication of covered interest rate parity

Use discount rate for relevant currency» It does not matter which one you take

Use consensus forecast of market» Don’t delude yourself by taking a “view” on exchange rates

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The Limitations of Simple NPV

Aim: Analyse risky projects under circumstances where uncertainty can

be managed.

Simple NPV-Analysis: Treat investment as one-off decision:

» Project stays constant; cannot be adapted. Treat uncertainty as an exogenous factor

Decision Trees and real options Managers respond to risk-factors: Integrate strategy and capital budgeting

» What is the value of flexibility and responsiveness?

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Investment under Uncertainty:The Simple NPV Rule

0 1 2 ... T ... Period

Initial

Investment

I

120

80

120 120

80 80

...

...

...

...

Revenueif Demandis high

Revenue

if Demandis low

50%

50%

Cost of Capital = 10%

NPV = - I + 100/0.1 = 1000 - I

Invest if I < 1000

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Investment under Uncertainty: Delay

0 1 2 ... T ... Period

- I

0

120 120

0 0

...

...

...

...

Revenueif Demandis high

Revenueif Demandis low

50%

50%

Strategy: Wait one Period

Case 1: I > 800, do not invest if demand is low

NPV =0.51.1

( - I + 1201.1

+ 1201.12

+ ... ) = 1200 - I2.2

0

0

Demand

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Investment under Uncertainty: Delay (2)

0 1 2 ... T ... Period

- I

- I

120 120

80 80

...

...

...

...

Revenueif Demandis high

Revenueif Demandis low

50%

50%

Strategy: Wait one Period

Case 2: I < 800, always invest

NPV =1

1.1( - I + 100

1.1+ 100

1.12+ ... ) = 1000 - I

1.1

Demand

0

0

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Summary of Strategies

Decision rule NPV

(1) Simple NPV 1000 - I

(2) Delay if I > 800

(3) Delay if I < 800

Delay is never optimal if I < 800 Delay is better than investing now if I > 833 Investment is never optimal if I > 1200

1200 - I

2.2

1000 - I

1.1

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Comparison of both Strategies

1000 - I

NPV

I

1000

909

0

0 833 1000 1200

I > 1200:

833 < I < 1200:

I < 833:

Never invest

Wait; invest if demand is high

Invest now

(1000 - I)/1.1

800

181 (1200-I)/2.2

Vertical distance= value of flexibility

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1 If 833 < I < 1000

Investment now has positive NPV = 1000 - I

However: Waiting is optimal in order to see how uncertainty overdemand resolves.

» Benefits from waiting: receive information to avoid loss.» Costs of waititng: delay of receiving cash flows.

Investment in positive NPV projects is not always optimal:

the flexibility gained from waiting has a positive value.

Note: Critical point is 833, not 800, why?

Results of Comparison (1)

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2 If 1000 < I < 1200

Investment now has negative NPV.

However: The project should not be abandoned: if demand

turns out high later, it has a positive NPV.

Negative NPV-projects should be delayed,

but not always be dismissed.

Results of Comparison (2)

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The project can be broken down into two components:» The investment possibility itself

– Has a Simple NPV of 1000-I» The flexibility of the project from the option to delay investment

Value of Flexibility is:

= Max (Value of investment later - Value of investing now, 0) Total NPV is the value of the whole project:

Total NPV = Simple NPV + Value of Flexibility» Investing immediately ignores that option of delay is valuable» Decisions must be based on total NPV

The value of flexibility is never negative

Total NPV leads always to the correct decision

Total NPV and Simple NPVIncorporating the Value of Flexibility

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If I<833, invest now, hence option to delay has no value. If 1000>I>833, then:

» Value of investing now = 1000 - I» Expected value of investing later is (1200-I)/2.2» Value of flexility is then:

So, with I=833, the value of flexibility is zero (why?), with I=1000 it increases to 91.

If 1200> I>1000, the value of flexibility is simply (1200-I)/2.2.» How does this change if the investment becomes more

risky?

Compute the Value of Flexibility

1200

2 21000

12 1000

2 2

II

I

.( )

.

.

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How to Use Total NPV

Assume I=900>833, hence value of flexibility positive. » Value of following optimal strategy = Total NPV» Value of investing now = Simple NPV» Value of flexibility = 80/2.2=36.4» Should you invest now?

Investing now gives 1000-900=100,» Simple NPV =100>0

Investing later gives:» Total NPV = Simple NPV + Value of Flexibility

= 100 + 36.4 = 136.4 Total NPV > Simple NPV, therefore delay!

» Deciding on the basis of Simple NPV ignores that investing now “kills the option”;

» Base decision always on Total NPV!

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The Impact of Volatility

How does the value of flexibility depend on uncertainty? Compare previous case with situation of more volatile prices:

Revenue (High Demand) = 150

Revenue (Low Demand) = 50

Expected revenue is unchanged ( = 100).

Volatility is higher.

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Flexibility in a Volatile Environment

Value ofFlexibility

I0 833 1000 1200 1500

250

0

Prices 150/50

Prices 120/80

583

Flexibility has a higher value in a more volatile environment

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The Option to Abandon

Assume same scenario as before, but no option to delay

Revenue (High Demand) = 120

Revenue (Low Demand) = 80

Investment outlay I = 1010

If there is no option to delay, NPV=1000-I=-10» Do not invest!

Assume assets have a scrap value:» At the end of the period:scrap value = 910» After the first period: scrap value = 0

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High revenue state (120):» PV (Cash Flow) = 1200 > 910 » Continue after period 1!» Receive: 1200 + 120 in period 1

Low revenue state (80):» PV (Cash Flows) = 800 < 910» Divest and abandon project in period 1!» Receive: 910 + 80 in period 1

With option to abandon, NPV=40

Invest: Option to abandon makes the project viable.

The Option to Abandon

PV = 910 + 80

1.10 5

1200 120

110 5 1050 1010.

..

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The Value of InformationHow to value a test market

Strategy D: - Introduce the product directly.

- Receive the cash flows immediately.

- If product is not accepted, launching costs are sunk.

Strategy T: - Introduce the product on a test market before launching it

for the whole market.

- Launch the product only if it is accepted in the test market;

costs for launching are only incurred in this case.

- Receive cash flows later.

Assumption: - The test market study gives you 100% reliable information

about the acceptance of the product.

Question: - How much are you willing to pay for a test market study?

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Example: Revenue if product is accepted: 10

Revenue if it is not accepted: 5

Both cases are equally likely.

Cost of launching the product: 60

Discount rate = 10%

Strategy D:

Strategy T:

Value of test market = 18.2 - 15 = 3.2

Value a Test MarketAn Example

NPV = 0.5 10

0.1 0 5

5

0 160 15.

.

NPV

0 5

11

10

0 160 0 18 2

.

. ..

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Flexibility and Project Design

Many projects have built-in flexibility:» Options to contract or expand.» Possibility to abandon if the assets have values outside the

project (secondary market).» Development opportunities:

– Sequence of models of the same product.– Oil fields.

In many cases the project can be designed to be more flexible:» Leasing contracts.» Make or buy decisions.» Scale versus adaptability.

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Natural Resource Investments

Your company has a two year lease to extract copper from a deposit. » Contains 8 million pounds of copper.» 1-year development phase costs $1.25m immediately.» Extraction costs of 85 cents per pound would be paid to a

contractor in advance when production begins» 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%.

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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

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Option Analysis

0 1

-1.25 Max[S1-0.85,0]

0.85 S1

Payoff

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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

ln .

ln..

. . ( . )

..

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

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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

36

Shutdown and Restart Options

{

}

C

O

Gold PriceP2P1

Present Value ofOpen Mine

Present Value of Closed Mine

PresentValue

37

Conclusions

Decision Tree Analysis modifies the simple NPV-rule:

The simple NPV rule gives generally not the correct conclusion if uncertainty can be “managed”.

The value of flexibility must be taken into account explicitly (cost of “killing an option”).

Properly calculated NPV remains the correct tool for decisions and evaluation of alternative strategies.