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© Copyright 2003, Alan Marshall 1
Real OptionsReal Options
© Copyright 2003, Alan Marshall 2
Real OptionsReal Options
Corporate ValuationCapital Budgeting
Value of Follow-on OpportunitiesValue of WaitingAbandonment Options
© Copyright 2003, Alan Marshall 3
The Value of Risky DebtThe Value of Risky Debt
For simplicity, we shall assume zero-coupon debt with a maturity value, MWe shall define D and the value ofrisky debt and Drf as the value of riskfree debt
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© Copyright 2003, Alan Marshall 4
Risky DebtRisky Debt
( )
( )rf
Nf
rf
ND
DDr1
MD
r1MD
<
+=
+=
© Copyright 2003, Alan Marshall 5
Risky DebtRisky Debt
The difference between these valuesis the value of the Put Option, PD,that the Debt holders have sold theEquity holdersThis put option allows the Equityholders to sell the firm to the Debtholders for M if VN < M
© Copyright 2003, Alan Marshall 6
Equity ValuationEquity Valuation
The value of the firm’s levered firm’sequity, EL, is:
EL = V - D= V - [Drf - PD]
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© Copyright 2003, Alan Marshall 7
Equity ValuationEquity Valuation
If at the maturity date of the debt, N,the value of the firm is less than thedebt’s maturity value, VN < M, thenthe Equity holders will not pay thedebt, and let the Debt holders takeover the firm
© Copyright 2003, Alan Marshall 8
Equity ValuationEquity Valuation
Therefore, we can see that the equityof the levered firm can be viewed as acall option on the firm’s assets withan exercise price of MTherefore:
EL = C
© Copyright 2003, Alan Marshall 9
Put-Call ParityPut-Call Parity
This follows directly from Put-Callparity:
EL = CC = V - DC = V - [Drf - PD]C + Drf = V + PD <- Put-Call Parity
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© Copyright 2003, Alan Marshall 10
Capital BudgetingCapital Budgeting
Value of Follow-on OpportunitiesGaining a foothold so that future projectsare possible
Value of Waiting
Abandonment Options
© Copyright 2003, Alan Marshall 11
Follow-on OpportunitiesFollow-on Opportunities
Suppose your firm is evaluating theLev-I, a personal levitation transportdevice. The cash flows are shown onthe next slide
They are extremely simplified, but that isnot important to what we are illustrating
© Copyright 2003, Alan Marshall 12
LevLev-I Project Cash Flows-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)
5
© Copyright 2003, Alan Marshall 13
Why We Might AcceptWhy We Might Accept
We want to preempt the competitionfrom entering the PLTD market whichwe believe will be highly profitable inthe long runThe Lev-I might teach us things thatwill be useful for developing the nextgeneration Lev-II
© Copyright 2003, Alan Marshall 14
LevLev-II -II CashflowsCashflows
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%
© Copyright 2003, Alan Marshall 15
Proceed?Proceed?
The Lev-II doesn’t look any betterThe NPV is twice as bad as the Lev-IThis business does not lookpromising!
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© Copyright 2003, Alan Marshall 16
The The LevLev-II as an Option-II as an Option
Undertaking the Lev-I gives us anoption to do the Lev-II, which will notbe available without the Lev-ICan we value the option?
© Copyright 2003, Alan Marshall 17
Call Option ValuationCall Option Valuation
TdT
2T
XeSln
d
T2T
XeSln
d
)d(NXe)d(NSC
1
2
rT
2
2
rT
1
2rT
1
σ−=σ
σ−
=
σ
σ+
=
⋅−⋅=
−
−
−
© Copyright 2003, Alan Marshall 18
CommentComment
This may look a bit different:No rfT term in the d1 and d2 calculationXe-rt, not X, in the denominator of thelogarithmThe result is the same, but a bit moreelegant
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© Copyright 2003, Alan Marshall 19
Option Valuation ParametersOption Valuation Parameters
BSOPM ParametersValue
S Today's PV of the cash flows 1,248.43X Cost (Investment) of the Project 3,000.00rf Risk free rate 10% T Term of the option (Years) 4σ Standard Deviation (assumed) 50%
© Copyright 2003, Alan Marshall 20
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
© Copyright 2003, Alan Marshall 21
Re-evaluating the Re-evaluating the LevLev-I-I
The DCF valuation of the Lev-I was(205.63)The Lev-II option is worth 305.30With the Lev-II option, the Lev-I isworth 99.67 > 0, accept
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© Copyright 2003, Alan Marshall 22
How Can It Be So Valuable?How Can It Be So Valuable?
The option valuation only considersthose outcomes that will result inpositive NPVs for the Lev-IIIf we get to 2008 and find theexpected cash flows are better thanwe anticipated, we will proceed withthe Lev-IIOtherwise, we do not proceed
© Copyright 2003, Alan Marshall 23
Cautionary NoteCautionary Note
Option theory can be used to justifyvery optimistic valuationsWhat happens is all of the firm’sprojects are accepted based on thevalue of options and none of theoptions expire in the money?
© Copyright 2003, Alan Marshall 24
Value of WaitingValue of Waiting
You have a claim that will allow yourfirm to obtain a 100% interest in anoil well by simply investing the $10million needed to develop the wellIf development has not begun by nextyear, the claim will expire and revertback to the government
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© Copyright 2003, Alan Marshall 25
Value of WaitingValue of Waiting
Currently, you forecast annualperpetual cash flows of $1.1 millionThe discount rate is 10%NPV = 1.1MM/10% - $10MM = $1MMThis is positive, so you could proceedimmediately
© Copyright 2003, Alan Marshall 26
Price UncertaintyPrice Uncertainty
Suppose that the price of oil is volatileIf the price of oil next year falls, theexpected perpetual annual cash flowswould be $0.8MM, resulting in aproject NPV of ($2MM)If the price rises, these cash flows willrise to $1.4MM, resulting in a projectNPV of $4MM
© Copyright 2003, Alan Marshall 27
First Year ReturnsFirst Year Returns
Low Price:(0.8MM + 8.0MM)/$10MM = -12%
High Price(1.4MM + 14MM)/$10MM = 54%
10
© Copyright 2003, Alan Marshall 28
Risk Neutral Expected ReturnRisk Neutral Expected Return
Assume an risk free rate of 10%Let πH be the probability of high price
The probability of low price is (1- πH)
E(r) =(-12%)(1-πH)+54%(πH) = 10% πH = 1/3
© Copyright 2003, Alan Marshall 29
Option to WaitOption to Wait
If you wait until next year, what is thewell be worth today?[(1/3)x4MM + (2/3)(0)]/(1.1) =$1.21MM, compared to the $1MM isdeveloped now
© Copyright 2003, Alan Marshall 30
Why Is Waiting Valuable?Why Is Waiting Valuable?
The passage of time resolvesuncertaintyIf a year from now, the conditionsdeteriorate, we can decide not toinvest in a bad projectWe are cutting of some of the left tailof the distribution
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© Copyright 2003, Alan Marshall 31
Abandonment OptionAbandonment Option
We can invest $12MM in a projectthat will generate gross margin of$1.7MM annually. This margin isexpected to grow at 9% annuallyFixed costs are $0.7MM annually andwill not grow.
© Copyright 2003, Alan Marshall 32
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%
© Copyright 2003, Alan Marshall 33
AbandonmentAbandonment
Ignored in the previous example isthe fact that there are many possibleoutcomes or paths where it may bebetter to stop the project and collectthe project salvage values.Suppose that $10MM of the $12MMproject cost is for fixed assets thathave a salvage value that declines at10% annually.
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© Copyright 2003, Alan Marshall 34
Building a Binomial TreeBuilding a Binomial Tree
Suppose that historically prices haveevolved according to a random walkwith a σ = 14%
87.015.1/1u/1d15.1eeu 14.0T
====== σ
© Copyright 2003, Alan Marshall 35
Risk Neutral Expected ReturnRisk Neutral Expected Return
With a risk free rate of 6%Let πH be the probability of high price
The probability of low price is (1- πH)
E(r) =(-13%)(1-πH)+15%(πH) = 6% πH = 0.6791
Note, there is a minor rounding error in thesource example
© Copyright 2003, Alan Marshall 36
Binomial TreeBinomial Tree
See the spreadsheet