Lecture Notes

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Lecture Notes

• December 1, 2003

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Application of Binomial Options Model

• Text, p. 649
• Global Real Estate Partners is doing a new
  project. If it succeeds, the value of the firm
  will be 650 if it fails, its value will be 250
• Current value of the firm is 400.
• Face value of debt is 300
• Interest rate is 7
• What are the values of the debt and equity?
• Note we arent told the probabilities of
  failure or success
• Reason we can estimate the risk-neutral
  probabilities from the value of the company

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Value of the firm
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First step

• Calculate risk-neutral probabilities
• Pretend investors are risk-neutral
• Expected value of the firm next year
• 400 1.07 428

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Calculating Risk-Neutral Probabilities

• Estimate pu by
• (Review this is derived by solving
• For pu)

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Second step calculate payoffs of debt and equity
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Third step Value debt and equity using
risk-neutral probabilities

• These add to 400 (allowing for roundoff error).

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Note the similarity

• between this problem and the options valuation
  problem.
• You know the payoffs of debt and equity
  separately. You can duplicate these payoffs by
  trading the stock of the firm and borrowing or
  lending. Therefore the current value of debt and
  equity must equal the current cost of the
  portfolio that generates the payoff of each.

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An example of multidate decision-making

• See text, p. 643
• Exoff Oil can buy oil land for 10,000
• Initial drilling costs are 500,000.
• Expected oil price is 20/barrel
• Real oil price is expected to stay constant
• Ongoing extraction costs 16/barrel
• Can extract 10,000 barrels/yr forever
• Discount rate 10
• Should Exoff buy the land?

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No

• Profit per barrel is 20 - 16 4.
• Capitalized value of revenues is 40,000/.10
  400,000
• Initial drilling costs land acquisition cost
  510,000.
• NPV -110,000.

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This may be the right answer to the wrong problem!

• Suppose that the price of oil will either rise to
  35 or drop to 5/barrel
• Exoff has the option to abandon the project if
  the price of oil drops
• If the probability that the price of oil will
  drop is ½, NPV of project is 440,000
• Payoff 1,390,000 if the price goes up,
  -510,000 if it drops.
• Whats the difference between the two diagrams?
• They are equivalent if Exoff has to continue the
  project regardless of the price of oil.

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Note the solution method

• Start from the end of the decision tree (the most
  distant future time) and work backward toward the
  present

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This still may be the wrong problem

• The way the diagram is drawn implies that the
  firm has to do initial drilling before knowing
  what happens to the price of oil.
• Suppose that it can postpone the initial drilling
  decision.
• Then the decision tree is different

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Heres the decision tree
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NPV is still higher

• Now its the average of 1,390,000 if the price
  of oil goes up, and -10,000 if it drops
• Whats the difference? In this scenario the firm
  doesnt bear initial drilling costs if the price
  of oil drops.
• NPV is now 690,000.

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Conclusion

• Depends on which of these diagrams correctly
  represent Exoffs options
• First diagram Exoff has to commit now to either
  (1) doing the initial drilling and extracting the
  oil forever, even if its unprofitable
• Second diagram Doing initial drilling before
  knowing whether extraction will be profitable,
  but having the option to shut down the operation
  if the price of oil drops
• Third diagram Having the option to postpone
  initial drilling

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Uncertainty and capital budgeting

• In the presence of uncertainty, it matters when
  decisions have to be made
• Careless use of expected values (certainty
  equivalents) will result in wrong decisions
• Analogy to options the essence of an option is
  that you can postpone the decision whether to
  exercise it or not.
• As in this exercise, having the option to
  postpone decisions is very important.