© Copyright 2004, Alan Marshall1 Real Options in Capital Budgeting

© Copyright 2004, Alan Marshall2 Capital Budgeting >Value of Follow-on Opportunities Gaining a foothold so that future projects are possible >Value of Waiting >Abandonment Options

© Copyright 2004, Alan Marshall3 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 Marshall4 Lev-I Project Cash Flows

© Copyright 2004, Alan Marshall5 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 Marshall6 Lev-II Cashflows

© Copyright 2004, Alan Marshall7 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 Marshall8 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 Marshall9 Call Option Valuation

© Copyright 2004, Alan Marshall10 Option Valuation Parameters

© Copyright 2004, Alan Marshall11 Option Valuation

© Copyright 2004, Alan Marshall12 Re-evaluating the Lev-I >The DCF valuation of the Lev-I was (205.63) >The Lev-II option is worth >With the Lev-II option, the Lev-I is worth > 0, accept

© Copyright 2004, Alan Marshall13 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 Marshall14 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 Marshall15 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 Marshall16 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 Marshall17 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 Marshall18 First Year Returns >Low Price: (0.8MM + 8.0MM)/$10MM = -12% >High Price (1.4MM + 14MM)/$10MM = 54%

© Copyright 2004, Alan Marshall19 Risk Neutral Expected Return >Assume an risk free rate of 10% >Let  H be the probability of high price The probability of low price is (1-  H ) E(r)=(-12%)(1-  H )+54%(  H ) = 10%  H = 1/3

© Copyright 2004, Alan Marshall20 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 Marshall21 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 Marshall22 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 Marshall23 DCF Analysis

© Copyright 2004, Alan Marshall24 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 Marshall25 Building a Binomial Tree >Suppose that historically prices have evolved according to a random walk with a  = 14%

© Copyright 2004, Alan Marshall26 Risk Neutral Expected Return >With a risk free rate of 6% >Let  H be the probability of high price The probability of low price is (1-  H ) E(r)=(-13%)(1-  H )+15%(  H ) = 6%  H = >Note, there is a minor rounding error in the source example

© Copyright 2004, Alan Marshall27 Binomial Tree >See the spreadsheet

© Copyright 2004, Alan Marshall28 Discussion >Again, the value is created by the flexibility of being able to eliminate the unfavourable results or branches