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Session 04Session 04Real Options Analysis ofReal Options Analysis of
Capital Investment ProposalsCapital Investment Proposals
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OBJECTIVEOBJECTIVE
In Reality, the managers has flexibility to revise their investment proposals as new information arrives. How do you handle such managerial options in CIA?
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OverviewOverviewManagerial options (Real option analysis)Summary
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Approaches To Dealing with Uncertainty and Approaches To Dealing with Uncertainty and Complexity in CIPComplexity in CIP
1. Traditional Approaches Simulation
Can’t handle well asymmetries in the distributions introduced by management's flexibility
Decision tree analysisNumber of different paths on the tree increases
geometrically.
Choice of discount rate: Risk of project may change over time.
2. Real Options ApproachThis approach circumvents the discount rate problem by
constructing a riskfree hedge.
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Difficulties with SimulationDifficulties with Simulation
A. Difficult to interpret a distribution of NPVs. Traditional view of NPV as "increase in shareholder
wealth from accepting the project" not applicable. Solution: Use simulation to assess the distribution of the net cashflows.
B. Problems in specifying interdependencies in step 1. C. Can’t handle well asymmetries in the distributions
introduced by management's flexibility to revise its prior
operating strategy as more information about project cashflows becomes available over time: -
Solution: Real Options.
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Decision tree analysisDecision tree analysis
Helps structure the managerial decision problem by mapping out feasible managerial alternatives in response to future events.
Pro:Forces management to recognize its implied operating strategy and the interdependencies between the initial and subsequent decisions.
Cons:A. Number of different paths on the tree increases geometrically.
B. Choice of discount rate:
Risk of project may change over time. (Options based approach circumvents the discount rate problem by constructing a riskfree hedge.)
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Real optionsReal options
One of the fundamental insights of modern finance theory is that options have value.
The phrase “We are out of options” is surely a sign of trouble.
Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation.
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What is a real option?What is a real option?
Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions.
Alert managers always look for real options in projects.
Smarter managers try to create real options.
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NPV Analysis and Real optionsNPV Analysis and Real options
“Traditional NPV analysis tends to ______________ the true value of a capital budgeting project.”
Underestimate OR overestimate ?
Why?
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Corporate OptionsCorporate Options4 types of “Real Options”
The opportunity to make follow-up investments (Growth) (has value if demand turns out to be higher than expected)Expansion of existing product lineNew productsNew geographic markets
The opportunity to “wait” and invest later (timing). It has value if the underlying variables are changing with a favorable trend.
Abandonment options (Has value if demand turns out to be lower than expected)ContractionTemporary suspension
Opportunity to vary the firm’s output or production methods. (Flexibility)
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Defer
Expand or contract
Abandon
Switch inputs or outputs
Grow
To wait before taking an action until more is known or timing is expected to be more favorable
To increase or decrease the scale of an operation in response to demand
To discontinue an operation and liquidate the assets
To commit investment in stages giving rise to a series of valuations and abandonment options
To alter the mix of inputs or outputs of a production process in response to market prices
Stage investment
To expand the scope of activities to capitalize on new perceived opportunities
ExamplesDescriptionOption
Adding or subtracting to a service offering, or adding memory to a computer
When to introduce a new product, or replace an existing piece of equipment
Discontinuation of a research project, or product/service line
Staging of research and development projects or financial commitments to a new venture
The output mix of telephony/internet/cellular services
Extension of brand names to new products or marketing through existing distribution channels
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Discounted CF and OptionsDiscounted CF and Options
We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.
M = NPV + Opt
A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time, the more versatile machine is more valuable because it comes with options.
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Value of “Real Option” = NPV with option - NPV without option
Corporate OptionsCorporate Options
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The Option to Expand (or Contract)The Option to Expand (or Contract)
Mgmt of a company considers entering into a market for a newly developed product. Market size is small in first two years and become very large afterwards.
Lack of economies of scale during first two years lead to negative NPV. Reject?
First mover advantage comes with first-stage investment.
Managements have an option to make a follow-up investment with the current proposal of setting up a small plant.
NPV of this option may offset the NPV of small plant to make overall investment proposal worthwhile.
Project Worth = -3.0 + 5.5 = 2.5
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Abandoning a project after it has been undertaken consist of selling the project’s assets or employing them in another area.
For certain projects, abandonment value is zero.Project should be abandoned when
its abandonment value exceeds the PV of Future CFsDivestment
Option to AbandonOption to Abandon
Project worth = NPV w/o AO + Value of AOProject worth = NPV w/o AO + Value of AO
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Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?
Use a discount rate of 10%
Option to AbandonOption to Abandon
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Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?
Option to AbandonOption to Abandon
Year 0 Year 1 Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 145
70 (.6)
50 (.4)
40 (.4)
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Option to AbandonOption to Abandon
Year 0 Year 1 Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 162
150 (.4)
Option Value =
162 - 145 =
$17 mil
Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?
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Option to Abandon – An exampleOption to Abandon – An example
Suppose we are drilling an oil well. The drilling rig costs $300 today, and in one year the well is either a success or a failure.
The outcomes are equally likely. The discount rate is 10%.
The PV of the successful payoff at time one is $575.
The PV of the unsuccessful payoff at time one is $0.
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Option to Abandon – An exampleOption to Abandon – An example
Traditional NPV analysis would indicate rejection of the project.
=Expected Payoff
Prob. Success
× Successful Payoff
+ Prob. Failure
× Failure Payoff
Expected Payoff
= (0.50×$575) + (0.50×$0) = $287.50
NPV = = –$38.641.10
$287.50–$300 +
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The Option to Abandon: ExampleThe Option to Abandon: Example
The firm has two decisions to make: drill or not, abandon or stay.
Do not drill
Drill
0$NPV
500$
Failure
Success: PV = $500
Sell the rig; salvage value
= $250
Sit on rig; stare at empty hole:
PV = $0.
Traditional NPV analysis overlooks the option to abandon.
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The Option to Abandon: ExampleThe Option to Abandon: Example
When we include the value of the option to abandon, the drilling project should proceed:
NPV = = $75.001.10
$412.50–$300 +
Expected Payoff
= (0.50×$575) + (0.50×$250) = $412.50
=Expected Payoff
Prob. Success
× Successful Payoff
+ Prob. Failure
× Failure Payoff
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Valuing the Option to AbandonValuing the Option to Abandon
Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.
M = NPV + Opt
$75.00 = –$38.64 + Opt
$75.00 + $38.64 = Opt
Opt = $113.64
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TO PROCEED OR ABANDON?
We are examining a new project. We expect to sell 7,000 units per year at $60 net cash flow apiece for the next 10 years. (the annual operating cash flow is projected at $60 * 7000 = $42,000. The relevant discount rate is 16% and the initial investment required is $1,750,000.
a) What is the base-case NPV?
b) After the first year, the project can be dismantled and sold for $1,500,000. If expected sales are revised based on the first year’s performance, when would it make sense to abandon the investment? (at what level of expected sales would it make sense to abandon the project?)
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EXPANSION ?
Applied Nanotech is considering introduction of a new surface cleaning machine. The marketing department has come up with the estimate that the company can sell 10 units per year at $0.3 million net cash flow per unit for the next 5 years. The engineering department has come up with the estimate that developing the machine will take a $10 million investment. The finance department has estimated that a 25% discount rate should be used.
a) What is the base-case NPV?
b) If unsuccessful, after the first year the project can be dismantled and will have an after tax salvage value of $5 million. Also, after the first year, expected cash flows will be revised up to 20 units per year or to 0 units, with equal probability. What is the revised NPV?
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The Option to Delay: ExampleThe Option to Delay: Example
Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remains constant at $25,000, but since costs are declining, the NPV at the time of launch steadily rises.
The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.
2)10.1(
900,7$529,6$
Year Cost PV NPV t NPV 0
0 20,000$ 25,000$ 5,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 6,364$ 2 17,100$ 25,000$ 7,900$ 6,529$ 3 16,929$ 25,000$ 8,071$ 6,064$ 4 16,760$ 25,000$ 8,240$ 5,628$
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WHEN TO PROCURE?
Your company is deciding when to invest in a new machine. The new machine will increase cash flow by $280,000 per year. You believe the technology used in the machine has a 10-year life (no matter when you purchase the machine it will be obsolete in 10 years from now).
The machine is currently priced at $1,500,000. The cost of the machine will decline by $125,000 per year until it reaches $1,000,000, where it will remain. If your required rate of return is 12 per cent, should you purchase the machine? If so, when should you purchase it?
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Intrinsic Value
Option to WaitOption to Wait
Option Price
Stock Price
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Intrinsic Value + Time Premium = Option Value
Time Premium = Vale of being able to wait
Option to WaitOption to Wait
Option Price
Stock Price
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More time = More value
Option to WaitOption to Wait
Option Price
Stock Price
Intrinsic Value + Time Premium = Option Value
Time Premium = Value of being able to wait
Intrinsic value
Time premium
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The Black-Scholes Model: The Black-Scholes Model: NotationNotation
C = price of callP = price of putS = price of stockE = exercise priceT = time to maturity ln(.) = natural logarithme = 2.71828...
N(.) = cum. norm. dist’n The following are
annual, compounded continuously:
r = domestic risk free rate of interest
d = foreign risk free rate or constant dividend yield
σ = volatility
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The Black-Scholes Model: The Black-Scholes Model: EquationsEquations
21
21
1
2
2
2
1
21
ln
21
ln
dNEedNSeP
dNEedNSeC
TdT
TdrES
d
T
TdrES
d
rTdT
rTdT
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The Black-Scholes Model: The Black-Scholes Model: Equations (Forward Form)Equations (Forward Form)
EdNSedNeP
EdNSedNeC
T
TE
Se
d
T
TE
Se
d
TdrrT
TdrrT
Tdr
Tdr
21
21
2
2
2
1
21
ln
21
ln
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The Black-Scholes Model: The Black-Scholes Model: Equations (Simplified)Equations (Simplified)
TSTS
PC
dNdNSPC
d
PdNdNSeC
TdTd
SeE
dT
Tdr
39886.02
0 If
21
;21
If
21
21
21
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Determinants of Option Prices
Increases in: Call Put Stock Price, S Increase Decrease Exercise Price, E Decrease Increase Volatility, sigma Increase Increase Time to Expiration, T Ambiguous Ambiguous Interest Rate, r Increase Decrease Cash Dividends, d Decrease Increase
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What happens to the premium of the option price over the exercisevalue as the stock price rises?
The premium of the option price over the exercise value declines as the stock price increases.
This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.
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The stock underlying the call option provides no dividends during the call option’s life.
There are no transactions costs for the sale/purchase of either the stock or the option.
kRF is known and constant during the option’s life.
What are the assumptions of theBlack-Scholes Option Pricing Model?
(More...)
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Security buyers may borrow any fraction of the purchase price at the short-term risk-free rate.
No penalty for short selling and sellers receive immediately full cash proceeds at today’s price.
Call option can be exercised only on its expiration date.
Security trading takes place in continuous time, and stock prices move randomly in continuous time.
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V = P[N(d1)] - Xe -kRFt[N(d2)].
d1 = . t
d2 = d1 - t.
What are the three equations thatmake up the OPM?
ln(P/X) + [kRF + (2/2)]t
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What is the value of the following call option according to the OPM?
Assume: P = $27; X = $25; kRF = 6%;t = 0.5 years: 2 = 0.11
V = $27[N(d1)] - $25e-(0.06)(0.5)[N(d2)].
ln($27/$25) + [(0.06 + 0.11/2)](0.5)
(0.3317)(0.7071)
= 0.5736.
d2 = d1 - (0.3317)(0.7071) = d1 - 0.2345
= 0.5736 - 0.2345 = 0.3391.
d1 =
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N(d1) = N(0.5736) = 0.5000 + 0.2168 = 0.7168.
N(d2) = N(0.3391) = 0.5000 + 0.1327 = 0.6327.
Note: Values obtained from Excel using NORMSDIST function.
V = $27(0.7168) - $25e-0.03(0.6327) = $19.3536 - $25(0.97045)(0.6327) = $4.0036.
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Current stock price: Call option value increases as the current stock price increases.
Exercise price: As the exercise price increases, a call option’s value decreases.
What impact do the following para-meters have on a call option’s value?
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Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.)
Risk-free rate: Call option’s value tends to increase as kRF increases (reduces the PV of the exercise price).
Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).
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Value of a Call and Put Options with Strike = Current Stock Price
0
1
2
3
4
5
6
7
8
9
10
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0.00.10.20.30.40.50.60.70.80.91.0
Time-to-Maturity
Cal
l an
d P
ut
Pri
ce
call put
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Call and Put Prices as a Function of Volatility
0
1
2
3
4
5
6
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Volatility
Cal
l an
d P
ut
Pri
ces
call put
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Computing Implied Volatility
volatility 0.3154
call 10.0000strike 100.0000share 105.0000rate_dom 0.0500rate_for 0.0000maturity 0.2500
factor 0.0249
d_1 0.4675d_2 0.3098
n_d_1 0.6799n_d_2 0.6217
call_part_1 71.3934call_part_2 -61.3934
error 0.0000
Insert any number to start
Formula for option value minus the actual
call value
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Computing Implied Volatility
volatility 0.315378127101852
call 10strike 100share 105rate_dom 0.05rate_for 0maturity 0.25
factor =(rate_dom - rate_for + (volatility^2)/2)*maturity
d_1 =(LN(share/strike)+factor)/(volatility*SQRT(maturity))d_2 =d_1-volatility*SQRT(maturity)
n_d_1 =NORMSDIST(d_1)n_d_2 =NORMSDIST(d_2)
call_part_1 =n_d_1*share*EXP(-rate_for*maturity)call_part_2 =- n_d_2*strike*EXP(-rate_dom*maturity)
error =call_part_1+call_part_2-call
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Construction of Pat's Get Rich Portfolio
-120
-100
-80
-60
-40
-20
0
20
40
60
80
50 60 70 80 90 100 110 120 130 140 150
Share Price
Po
rtfo
lio
Val
ues
callP_ShareP_bondPortfolioTangent
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SummarySummary
Managerial options are important considerations in capital budgeting viz. Flexibility that mgmt has to alter a previously made decision.
Greater the uncertainty surrounding the use of an option, the greater its value.
A project’s worth can be viewed as its traditional NPV together with the value of managerial option.
Consideration of these corporate options can sometimes turn a reject decision into an accept decision and an accept decision into a decision to postpone.
