1. 1 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

2. 2 Overview l Topics in Capital Budgeting l Investments in international project »What are the cost of capital? »How do you assess risk and returns in foreign currencies? l Capital budgeting and stratetic decisions »Decision trees and real options

3. 3 Offshore Borrowing l 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. l 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. 4 Offshore Borrowing l 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. l Suppose the 5-year forward rate is 0.91632 AUD/CHF. l 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 l 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. l Hence nothing has been gained by borrowing offshore! »Why does this work?

5. 5 Covered Interest Rate Parity l This equivalence always holds and is known as covered interest rate parity:

6. 6 Proof By Arbitrage l 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. l 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. 7 International Capital Budgeting l 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 l How should you calculate the NPV?

8. 8 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$, gives NPV in C$.

9. 9 Results for Two Methods Method I: Present value = -Yen 49,230 Method II: Present value = -C$ 590 = -Yen (590*83.86)=-Yen49,230 l Both methods yield the same result! »Why is this necessary?

10. 10 Alternative Exchange Rate Forecast l 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?

11. 11 Capital Budgeting and Currency Speculation l 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). l 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 l 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

12. 12 Summary International Capital Budgeting l There is no easy gain from offshore borrowing »Implication of covered interest rate parity l Use discount rate for relevant currency »It does not matter which one you take l Use consensus forecast of market »Don ’ t delude yourself by taking a “ view ” on exchange rates

13. 13 The Limitations of Simple NPV Aim: l Analyse risky projects under circumstances where uncertainty can be managed. Simple NPV-Analysis: l Treat investment as one-off decision: »Project stays constant; cannot be adapted. l Treat uncertainty as an exogenous factor Decision Trees and real options l Managers respond to risk-factors: l Integrate strategy and capital budgeting »What is the value of flexibility and responsiveness?

14. 14 Investment under Uncertainty: The Simple NPV Rule 012...T Period Initial Investment I 120 80 120 80... Revenue if Demand is high Revenue if Demand is low 50% Cost of Capital = 10% NPV = - I + 100/0.1 = 1000 - I Invest if I < 1000

15. 15 Investment under Uncertainty: Delay 012...T Period - I 0 120 00... Revenue if Demand is high Revenue if Demand is low 50% Strategy: Wait one Period Case 1: I > 800, do not invest if demand is low NPV = 0.5 1.1 ( - I + 120 1.1 + 120 1.1 2 +... ) = 1200 - I 2.2 0 0 Demand

16. 16 Investment under Uncertainty: Delay (2) 012...T Period - I 120 80... Revenue if Demand is high Revenue if Demand is low 50% Strategy: Wait one Period Case 2: I < 800, always invest NPV = 1 1.1 ( - I + 100 1.1 + 100 1.1 2 +... ) = 1000 - I 1.1 Demand 0 0

17. 17 Summary of Strategies Decision ruleNPV (1)Simple NPV1000 - I (2)Delay if I > 800 (3)Delay if I < 800 l Delay is never optimal if I < 800 l Delay is better than investing now if I > 833 l Investment is never optimal if I > 1200

18. 18 Comparison of both Strategies 1000 - I NPV I 1000 909 0 083310001200 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

19. 19 1If 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? Results of Comparison (1)

20. 20 2If 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)

21. 21 l 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 l Value of Flexibility is: =Max (Value of investment later - Value of investing now, 0) l 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 NPV Incorporating the Value of Flexibility

22. 22 l If I<833, invest now, hence option to delay has no value. l 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. l 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

23. 23 How to Use Total NPV l 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? l Investing now gives 1000-900=100, »Simple NPV =100>0 l Investing later gives: »Total NPV= Simple NPV+ Value of Flexibility = 100 + 36.4= 136.4 l 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!

24. 24 The Impact of Volatility l How does the value of flexibility depend on uncertainty? l 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.

25. 25 Flexibility in a Volatile Environment Value of Flexibility I 0 833100012001500 250 0 Prices 150/50 Prices 120/80 583 Flexibility has a higher value in a more volatile environment

26. 26 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

27. 27 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

28. 28 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?

29. 29 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 Market An Example

30. 30 Flexibility and Project Design l 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. l In many cases the project can be designed to be more flexible: »Leasing contracts. »Make or buy decisions. »Scale versus adaptability.

31. 31 Natural Resource Investments l 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%.

32. 32 Standard Expected NPV Analysis

33. 33 Option Analysis 01 -1.25Max[S 1 -0.85,0] 0.85S1S1 Payoff

34. 34 Option Analysis

35. 35 Terminal Distribution Distribution of Copper Price at Time 1 0.00 0.50 1.00 1.50 2.00 2.50 0.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.801.902.00 Copper Price Probability Density

36. 36 Shutdown and Restart Options { } C O Gold Price P 2 P 1 Present Value of Open Mine Present Value of Closed Mine Present Value

37. 37 Conclusions Decision Tree Analysis modifies the simple NPV-rule: l The simple NPV rule gives generally not the correct conclusion if uncertainty can be “ managed ”. l The value of flexibility must be taken into account explicitly (cost of “ killing an option ” ). l Properly calculated NPV remains the correct tool for decisions and evaluation of alternative strategies.