Copyright © 2003 Pearson Education, Inc.Slide 17-1 Chapter 17 Real Options.

Copyright © 2003 Pearson Education, Inc. Slide 17-1

Chapter 17Chapter 17Real OptionsReal Options


Real options

•The application of derivatives theory to the operation and valuation of real investment projects

•A call option is the right to pay a strike price to receive the present value of a stream of future cash flows

•An investment project is the right to pay an investment cost to receive the present value of a future cash flow stream

Investment Project Call Option

Investment Cost = Strike Price

Present Value of Project = Price of Underlying Asset


Investment and the NPV rule

• NPV rule:– Compute NPV by discounting expected cashflows at the

opportunity cost of capital

– Accept a project if and only if its NPV is positive and it exceeds the NPV of all mutually exclusive alternative projects.

• Example under certainty: – Invest in a $10 machine, that will produce one widget/year forever

at a cost of $0.90/widget. The widget will sell at $0.55 next year and the price will increase at 4% per year. Risk-free rate is 5% per year. The investment can occur anytime. Should it? If yes, when?


Investment and the NPV rule (cont.)

• Example under certainty: (cont.)

– Static NPV:

NPVInvest today = $27

NPVWait five years = $30.49

NPVWait 23.82 years = $35.03

=$ .0 551

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Investment and the NPV rule (cont.)

• The project as an option:– The decision to invest is analogous to the decision to exercise an

American option early• Exercise price ~ investment cost• Underlying asset ~ value of the project

– Tradeoff between three factors: • Dividends foregone by not exercising: cashflows from selling widgets • Interest saved by deferring the payment of exercise price• Value of the insurance lost by by exercising (the implicit put option): since

no uncertainty, there is no insurance value

– S = $55 (=$0.55/(0.05-0.04)), K = $28 (=$10 + $0.90/0.05), r = 0.04879 (=ln1.05), = 0, = 0.0095669 (=ln1.05 – ln1.05) C = $35.03


Investment under uncertainty

• Example:– A project requires an intial investment of $100, and is expected to

generate a perpetual cashflow stream, with a first cash flow $18 in one year, expected to grow at 3% annually. Assume a discount rate of 15%. If the project can be delayed for up to two years, should the project be accepted? If yes, when?

– Static NPV: $18/(0.15 – 0.03) – $100 = $50

– Trade-off between three factors:• Foregone initial cashflow: $18

• Interest savings: $7 (7% x $100)

• Value of preserved insurance: Is it more than the loss due to delay?

Loss of $11 if delayed


Investment under uncertainty (cont.)

• Example: (cont.)

– What is the value of the insurance? Need to know the volatility of cashflows:


Investment under uncertainty (cont.)

• Example: (cont.)

– S = $150, K = $100, r = 6.766% (=ln1.07), = 0.5, t = 2 years, = 0.1133 (=ln(1+($18/$50))), p* = 0.335 C = $55.80 > $50


Real options in practice

• The decision about whether and when to invest in a project ~ call option

• The ability to shut down, restart, and permanently abandon a project ~ project + put option

• Strategic options: The ability to invest in projects that may give rise to future options ~ compound option

• Flexibility options: Ability to switch between inputs, outputs, or technologies ~ rainbow option


Real options in practice (cont.)

• Peak-load electricity generation– Plant idle when price of electricity is less than the cost of fuel

– Plant online when electricity price spikes or fuel price declines

– Similar to owning a strip of call options on electricity expiring daily, with a strike price of cost of variable inputs

– Spark spread: Selec – H x Sgas, where H is plant efficiency measure

– Profit = max(Selec – H x Sgas, 0), a European exchange option

–

– By rewriting using put-call parity:

Value of Plant ) BSCall F H F r t rE t G t ti

n

ii i i( , , , , ,, ,

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e F H F BSPut F H F r t rrt

E t G ti

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Static NPV Option Not to Operate



• Research and development– Costs incurred to acquire technology to be used in future projects

– Projects in the future only undertaken if they have positive NPV


Commodity extraction as an option

• Incur the extraction costs to realize the value of the resource: defer investment and stop and start production

• Example: Single-barrel extraction under certainty– A plot of land contains one barrel of oil that can be extracted by

paying $13.60. Currently, oil sells for $15/barrel, effective annual lease rate is 4%, and effective annual risk-free rate is 5%

– How much is the land worth? • $1.40 (= $15 – $13.60) [no real options, immediate extraction]

• $1.796 [considering real options, trigger price $16.918 at t = 12.575]

• If the lease rate of an extractive commodity is zero, it is best to leave the commodity underground forever


Commodity extraction as an option (cont.)

• Example: Single-barrel extraction under uncertainty– The same example as before, but oil price volatility is 15%

– How much is the land worth? • $3.7856 [considering real options, trigger price $25.3388]

• When uncertainty is introduced, the optimal exercise time is later, and the project value, and trigger price is higher



• Example: Valuing an infinite oil reserve– Example 17.1: Suppose S0 = $15, r = 5%, = 4%, c = $8, and the

investment cost I is $180• The value of the producing well is $15/0.04 – $8/0.05 = $215.

• Per barrel extraction cost is (c/r + I) = $13.60

• CallPerpetual [$15/0.04, $8/0.05 + 180, 0.000001, ln(1.05), ln(1.04)]

= [$44.914, $422.956]

• The value of the well is $422.956

• Extraction occurs when S = 0.04 x $422.956 = $16.918

– Example 17.2: Assumptions above + oil price volatility = 0.15• CallPerpetual [$15/0.04, $8/0.05 + 180, 0.15, ln(1.05), ln(1.04)]

= [$94.639, $633.469]


Commodity extraction with the option to shut down and restart production


Commodity extraction with the option to shut down and restart production (cont.)

Copyright © 2003 Pearson Education, Inc.Slide 17-1 Chapter 17 Real Options.

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