© Copyright 2004, Alan Marshall1 Real Options in Capital Budgeting

© Copyright 2004, Alan Marshall 1

Real OptionsReal Optionsin Capital Budgetingin Capital Budgeting


Capital BudgetingCapital Budgeting

> Value of Follow-on Opportunities• Gaining a foothold so that future projects are

possible

> Value of Waiting

> Abandonment Options


Follow-on OpportunitiesFollow-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


Lev-I Project Cash FlowsLev-I Project Cash Flows

Lev-I PLTD Project

2004 2005 2006 2007 2008After-tax OCF 500 500 500 500PV @ 20% 1,294.37Investment 1,500.00NPV (205.63)


Why We Might AcceptWhy 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


Lev-II CashflowsLev-II Cashflows

Lev-II PLTD Project

2004 … 2008 2009 2010 2011 20121000 1000 1000 1000

PV @ 20% 1,248.43 2,588.73Investment 2,049.04 3,000.00NPV (800.62) (411.27)

Note: Since the investment in 2008 is fixed and known, weare discounting it at the risk free rate of 10%


Proceed?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!


The Lev-II as an OptionThe 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?


Call Option ValuationCall Option Valuation

TdT

2T

XeS

lnd

T

2T

XeS

lnd

)d(NXe)d(NSC

1

2

rT

2

2

rT

1

2rT

1


Option Valuation ParametersOption Valuation Parameters

BSOPM ParametersValue

S Today's PV of the cash flows 1,248.43

X Cost (Investment) of the Project 3,000.00

rf Risk free rate 10%

T Term of the option (Years) 4 Standard Deviation (assumed) 50%


Option ValuationOption Valuation

BSOPM CalculatorExercise 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


Re-evaluating the Lev-IRe-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


How Can It Be So Valuable?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


Cautionary NoteCautionary 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?


Value of WaitingValue 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


Value of WaitingValue 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


Price UncertaintyPrice 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


First Year ReturnsFirst Year Returns

> Low Price:• (0.8MM + 8.0MM)/$10MM = -12%

> High Price• (1.4MM + 14MM)/$10MM = 54%


Risk Neutral Expected ReturnRisk 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


Option to WaitOption 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


Why Is Waiting Valuable?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


Abandonment OptionAbandonment 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.


DCF AnalysisDCF Analysis

Project Abandonment Example

YEAR 0 1 2 3 4 5 6 7 8 9 10Forecast Revenues 1.85 2.02 2.20 2.40 2.62 2.85 3.11 3.39 3.69 4.02Present value 17.00Fixed Costs 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70Present value 5.15NPV (0.15)

Investment = 12 Note Since fixed costs are not uncertain,Year 1 cash flow = 1.7 they are evaluated at the risk free rate

Cash flow growth = 9.00%Fixed costs = 0.7

Discount rate = 9.00%

RF = 6.00%


AbandonmentAbandonment

> 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.


Building a Binomial TreeBuilding a Binomial Tree

> Suppose that historically prices have evolved according to a random walk with a = 14%

87.015.1/1u/1d

15.1eeu 14.0T


Risk Neutral Expected ReturnRisk 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 = 0.6791

> Note, there is a minor rounding error in the source example


Binomial TreeBinomial Tree

> See the spreadsheet


DiscussionDiscussion

> Again, the value is created by the flexibility of being able to eliminate the unfavourable results or branches

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© Copyright 2004, Alan Marshall1 Real Options in Capital Budgeting