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Real Options in Capital Budgeting © Copyright 2004, Alan Marshall 1 Capital Budgeting > Value of Follow-on Opportunities • Gaining a foothold so that future projects are possible > Value of Waiting > Abandonment Options © Copyright 2004, Alan Marshall 2 Follow-on Opportunities > Suppose your firm is evaluating the Lev-I, a personal levitation transport device. The cash flows are shown on the next slide • They are extremely simplified, but that is not important to what we are illustrating © Copyright 2004, Alan Marshall 3 Lev-I Project Cash Flows Lev-I PLTD Project 2004 After-tax OCF PV @ 20% 1,294.37 Investment 1,500.00 NPV (205.63) © Copyright 2004, Alan Marshall 2005 500 2006 500 2007 500 2008 500 4 Why We Might Accept > We want to preempt the competition from entering the PLTD market which we believe will be highly profitable in the long run > The Lev-I might teach us things that will be useful for developing the next generation Lev-II © Copyright 2004, Alan Marshall 5 Lev-II Cashflows Lev-II PLTD Project 2004 … PV @ 20% 1,248.43 Investment 2,049.04 (800.62) NPV 2008 2009 1000 2010 1000 2011 1000 2012 1000 2,588.73 3,000.00 (411.27) Note: Since the investment in 2008 is fixed and known, we are discounting it at the risk free rate of 10% © Copyright 2004, Alan Marshall 6 Proceed? > The Lev-II doesn’t look any better > The NPV is twice as bad as the Lev-I > This business does not look promising! © Copyright 2004, Alan Marshall 7 The Lev-II as an Option > Undertaking the Lev-I gives us an option to do the Lev-II, which will not be available without the Lev-I > Can we value the option? © Copyright 2004, Alan Marshall 8 Call Option Valuation C S N(d1) Xe rT N(d2 ) S T ln rT Xe 2 d1 T 2 S T ln rT Xe 2 d2 d1 T T 2 © Copyright 2004, Alan Marshall 9 Option Valuation Parameters BSOPM Parameters S Today's PV of the cash flows Value 1,248.43 X Cost (Investment) of the Project 3,000.00 rf Risk free rate T Term of the option (Years) Standard Deviation (assumed) © Copyright 2004, Alan Marshall 10% 4 50% 10 Option Valuation BSOPM Calculator Exercise Price of Option $3,000.00 Current Price of Underlying $1,248.43 Annualized Standard Deviation 50.00% Annual Riskfree Rate 10.00% Term to Expiry (in Years) 4.0000 Call Price $305.30 © Copyright 2004, Alan Marshall 11 Re-evaluating the Lev-I > The DCF valuation of the Lev-I was (205.63) > The Lev-II option is worth 305.30 > With the Lev-II option, the Lev-I is worth 99.67 > 0, accept © Copyright 2004, Alan Marshall 12 How Can It Be So Valuable? > The option valuation only considers those outcomes that will result in positive NPVs for the Lev-II > If we get to 2008 and find the expected cash flows are better than we anticipated, we will proceed with the Lev-II > Otherwise, we do not proceed © Copyright 2004, Alan Marshall 13 Cautionary Note > Option theory can be used to justify very optimistic valuations > What happens is all of the firm’s projects are accepted based on the value of options and none of the options expire in the money? © Copyright 2004, Alan Marshall 14 Value of Waiting > You have a claim that will allow your firm to obtain a 100% interest in an oil well by simply investing the $10 million needed to develop the well > If development has not begun by next year, the claim will expire and revert back to the government © Copyright 2004, Alan Marshall 15 Value of Waiting > Currently, you forecast annual perpetual cash flows of $1.1 million > The discount rate is 10% > NPV = 1.1MM/10% - $10MM = $1MM > This is positive, so you could proceed immediately © Copyright 2004, Alan Marshall 16 Price Uncertainty > Suppose that the price of oil is volatile > If the price of oil next year falls, the expected perpetual annual cash flows would be $0.8MM, resulting in a project NPV of ($2MM) > If the price rises, these cash flows will rise to $1.4MM, resulting in a project NPV of $4MM © Copyright 2004, Alan Marshall 17 First Year Returns > Low Price: • (0.8MM + 8.0MM)/$10MM = -12% > High Price • (1.4MM + 14MM)/$10MM = 54% © Copyright 2004, Alan Marshall 18 Risk Neutral Expected Return > Assume an risk free rate of 10% > Let pH be the probability of high price • The probability of low price is (1- pH) E(r) =(-12%)(1-pH)+54%(pH) = 10% pH = 1/3 © Copyright 2004, Alan Marshall 19 Option to Wait > If you wait until next year, what is the well be worth today? > [(1/3)x4MM + (2/3)(0)]/(1.1) = $1.21MM, compared to the $1MM is developed now © Copyright 2004, Alan Marshall 20 Why Is Waiting Valuable? > The passage of time resolves uncertainty > If a year from now, the conditions deteriorate, we can decide not to invest in a bad project > We are cutting of some of the left tail of the distribution © Copyright 2004, Alan Marshall 21 Abandonment Option > We can invest $12MM in a project that will generate gross margin of $1.7MM annually. This margin is expected to grow at 9% annually Fixed costs are $0.7MM annually and will not grow. © Copyright 2004, Alan Marshall 22 DCF Analysis Project Abandonment Example YEAR Forecast Revenues Present value Fixed Costs Present value NPV 0 17.00 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 5.15 (0.15) Investment = 12 Year 1 cash flow = 1.7 Cash flow growth = 9.00% Fixed costs = 0.7 Discount rate = 9.00% RF = 6.00% © Copyright 2004, Alan Marshall 1 2 3 4 5 6 7 8 9 10 1.85 2.02 2.20 2.40 2.62 2.85 3.11 3.39 3.69 4.02 Note Since fixed costs are not uncertain, they are evaluated at the risk free rate 23 Abandonment > Ignored in the previous example is the fact that there are many possible outcomes or paths where it may be better to stop the project and collect the project salvage values. > Suppose that $10MM of the $12MM project cost is for fixed assets that have a salvage value that declines at 10% annually. © Copyright 2004, Alan Marshall 24 Building a Binomial Tree > Suppose that historically prices have evolved according to a random walk with a = 14% ue T e 0.14 1.15 d 1/ u 1/ 1.15 0.87 © Copyright 2004, Alan Marshall 25 Risk Neutral Expected Return > With a risk free rate of 6% > Let pH be the probability of high price • The probability of low price is (1- pH) E(r) =(-13%)(1-pH)+15%(pH) = 6% pH = 0.6791 > Note, there is a minor rounding error in the source example © Copyright 2004, Alan Marshall 26 Binomial Tree > See the spreadsheet © Copyright 2004, Alan Marshall 27 Discussion > Again, the value is created by the flexibility of being able to eliminate the unfavourable results or branches © Copyright 2004, Alan Marshall 28