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International Project Evaluation and Real Options
Global Financial Management
Campbell R. HarveyFuqua School of Business
Duke [email protected]
http://www.duke.edu/~charvey
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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
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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
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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?
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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. ..
.
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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.
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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
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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.