International Project Evaluation and
Real Options
Global Financial Management
Campbell R. Harvey
Fuqua School of Business
Duke University
charvey@mail.duke.edu
http://www.duke.edu/~charvey
1
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
2
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
3
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?
4
Covered Interest Rate Parity

This equivalence always holds and is known as covered
interest rate parity:
FTAUD / CHF



1  r 
AUD T
1  rT
AUD / CHF
S0
CHF T
T
112
. 

0.91632  0.8
5
. 
109
5
5
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.
6
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$: 83.86
» Assumption: the investment is risk free
How should you calculate the NPV?
7
Two Ways of Calculating NPV
Method I
Method II
Step 1: Forecast cash flows in Yen
Step 1: Forecast cash flows in Yen
Step 2: Discount at interest rate for
Yen; gives NPV in Yen
Step 2: Convert cash flows into C$
using implied forward rate
Step 3: Convert NPV in Yen into
Canadian dollars at spot
exchange rate, gives NPV in
C$
Step 3: Discount C$ cash flows using
the interest rate for C$, gives
NPV in C$.
8
Results for Two Methods
Year
Forward rate
Method I
Cash flows (Yen)
Discount factor (Yen)
PV(Yen)
Method II
Cash flows (C$)
Discount factor (C$)
PV(C$)
1996
83.86
1997
79.35
1998
75.08
1999
71.04
2000
67.22
2001
63.61
2002
60.18
2003
56.95
-1300
200
200
200
200
200
200
200
1.000
0.972
0.944
0.918
0.892
0.867
0.842
0.819
-1300.000 194.363 188.886 183.562 178.389 173.362 168.476 163.728
-15.502
1.000
-15.502
2.520
0.920
2.318
2.664
0.846
2.252
2.815
0.778
2.189
2.975
0.715
2.127
3.144
0.657
2.067
3.323
0.605
2.009
3.512
0.556
1.952
Method I: Present value = -Yen 49,230
Method II: Present value = -C$ 590 = -Yen (590*83.86)=-Yen49,230

Both methods yield the same result!
» Why is this necessary?
9
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
Year
Time
Forward rate
Method I
Cash flows (Yen)
Discount factor (Yen)
PV(Yen)
Method II
Forward rate
Cash flows (C$)
PV(C$)
1996
0
83.86
1997
1
79.35
1998
2
75.08
1999
3
71.04
2000
4
67.22
2001
5
63.61
2002
6
60.18
2003
7
56.95
-1300
200
200
200
200
200
200
200
1.000
0.972
0.944
0.918
0.892
0.867
0.842
0.819
-1300.000 194.363 188.886 183.562 178.389 173.362 168.476 163.728
83.862
-15.502
-15.502
77.367
2.585
2.377
71.375
2.802
2.369
65.847
3.037
2.362
60.747
3.292
2.354
56.043
3.569
2.346
51.702
3.868
2.339
47.698
4.193
2.331
» Now the PV with Method II becomes C$ 976 or Yen 81,840
– Now the project looks profitable, should you take it?
10
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
11
Summary
International 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
12
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?
13
Investment under Uncertainty:
The Simple NPV Rule
0
1
120
2
120
...
...
T
120
...
Period
...
Revenue
if Demand
is high
...
Revenue
if Demand
is low
Initial
Investment
I
80
80
...
80
Cost of Capital = 10%
NPV = - I + 100/0.1 = 1000 - I
Invest if I < 1000
14
Investment under Uncertainty: Delay
Strategy: Wait one Period
Case 1: I > 800, do not invest if demand is low
0
1
2
...
T
...
Period
0
-I
120
...
120
...
Revenue
if Demand
is high
...
Revenue
if Demand
is low
Demand
0
NPV =
0
0
0.5
1.1
(-I+
120
1.1
...
+
120
1.12
+ ... ) =
0
1200 - I
2.2
15
Investment under Uncertainty: Delay
(2)
Strategy: Wait one Period
Case 2: I < 800, always invest
0
1
0
-I
2
...
120
...
T
120
...
Period
...
Revenue
if Demand
is high
...
Revenue
if Demand
is low
Demand
0
NPV =
-I
1
1.1
(-I+
80
100
1.1
...
+
100
1.12
+ ... ) =
80
1000 - I
1.1
16
Summary of Strategies
(1)
(2)
(3)



Decision rule
NPV
Simple NPV
1000 - I
Delay if I > 800
1200 - I
2.2
Delay if I < 800
1000 - I
1.1
Delay is never optimal if I < 800
Delay is better than investing now if I > 833
Investment is never optimal if I > 1200
17
Comparison of both Strategies
NPV
I > 1200:
Never invest
833 < I < 1200:
Wait; invest if demand is high
I < 833:
Invest now
1000
909
Vertical distance
= value of flexibility
181
0
I
0
800
833 1000
1200
18
Results of Comparison (1)
1 If 833 < I < 1000
Investment now has positive NPV = 1000 - I
However:
Waiting is optimal in order to see how uncertainty over
demand 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?
19
Results of Comparison (2)
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.
20
Total NPV and Simple NPV
Incorporating the Value of Flexibility



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
21
Compute the Value of Flexibility



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:
1200  I
1.2 I  1000
 ( 1000  I ) 
2.2
2.2
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?
22
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!
23
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.
24
Flexibility in a Volatile Environment
Value of
Flexibility
Prices 150/50
250
Prices 120/80
0
I
0
583
833
1000
1200
1500
Flexibility has a higher value in a more volatile environment
25
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
26
The Option to Abandon
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
PV =
910 + 80
1200  120
0 .5 
1.1
1.1
0 .5  1050  1010
With option to abandon, NPV=40
Invest: Option to abandon makes the project viable.
27
The Value of Information
How 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?
28
Value a Test Market
An Example
Example:
Revenue if product is accepted:
Revenue if it is not accepted:
Both cases are equally likely.
Cost of launching the product:
Discount rate =
Strategy D:
NPV = 0.5
Strategy T:
NPV 
0 .5
11
.
10
5
60
10%
10
5
 0 .5
 60  15
0.1
0 .1
 10

 60  0  18 .2

 0 .1

Value of test market = 18.2 - 15 = 3.2
29
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.
30
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%.
31
Standard Expected NPV Analysis
8( E[ S1 ]  0.85)
E[ NPV ]  125
. 
11
.
E[ ST ]  S0e T
E[ S1 ]  0.95e0.07  11089
.
8(10189
.
 0.85)
E[ NPV ]  125
. 
 0.022
11
.
32
Option Analysis
0
1
-1.25
Max[S1-0.85,0]
Payoff
0.85
S1
33
Option Analysis
C  SN(d1 )  Xe  rT N(d2 )


S

ln   rf  0.5 2 T
 X
d1 
 T
0.95

2
ln
  0.05  0.5(0.20) 1
 0.85
d1 
 0.906
0.20 1


d 2  d1   T  0.906  0.20  0.706
C  0.85N(0.906)  0.85e 0.05(1) N(0.706)  0162
.
34
Terminal Distribution
Distribution of Copper Price at Time 1
2.00
1.50
1.00
0.50
2.00
1.90
1.80
1.70
1.60
1.50
1.40
1.30
1.20
1.10
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.00
0.30
Probability Density
2.50
Copper Price
35
Shutdown and Restart Options
Present Value of
Open Mine
Present
Value
}
O
Present Value of
Closed Mine
{
C
P1
P2
Gold Price
36
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.
37