Options

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Options
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Exam prep item

• An firm has a project with NPVgt0 that costs a lot
  of money.
• It pays off after the owner dies.
• Should she invest? In the project? In financial
  assets? How?

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An investment opportunity that increases value.
Time one cash flow
NPV
Time zero cash flow
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Exam prep item

• What is the interest rate?

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Dont write

• The interest rate is the time value of money.

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Do write

• The interest rate is the premium for current
  delivery of money.
• P0 is the price of current money in current
  money, namely 1.
• P1 is the price of time-one money in terms of
  current money, something lt1.
• P

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Teaching evaluations

• Now

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Definition of a call option

• A call option is the right but not the obligation
  to buy 100 shares of the stock at a stated
  exercise price on or before a stated expiration
  date.
• The price of the option is not the exercise price.

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Example

• A share of IBM sells for 100.
• The call has an exercise price of 95.
• The price of the call should be at least 5.
• Actually, it will be more.

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Options of Microsoft

• Calls-Last Puts-Last
• Option and Strike
• NY Close Price July Oct. July Oct.
• Microsoft
• 90 3/8 85 9 3/4 - 3 1/2 -
• 90 3/8 95 4 3/4 - 8 -

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Why are options valuable?

• Options are insurance policies.
• In case a stock I dont hold goes up, I get part
  of the gain.
• Options are more valuable as the share price is
  more risky.
• Opposite of the share price, which is lower as
  the share is more risky.

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Compare

• Stock is at 50. In six weeks either 60 or 40,
  with equal probability.
• 1. Borrow 5000, buy 100 shares. In six weeks have
  either 1000 or -1000.
• 2. Buy 100 calls with exercise price 50. Cost
  about 200. In six weeks have either 800 or
  -200.
• Risk reduction, an insurance contract.

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Payoff from an option

• Forget the price of the option. Thats sunk
  cost.
• Look at the value at expiration.

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Payoff of a Call Option on the Expiration Date
Value of call (C)at expiration ()
Value of common stock (ST) at expiration ()
0
50
Exercise price
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Seldom exercise an option before expiration

• Sell it to someone else, instead.
• You no longer want the insurance.
• Someone else does.

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Application firm near bankruptcy

• Viewpoint of equity.
• Exercise price pay off the bond holders.
• If the firm is worth less than the bonds, equity
  gets zero.
• If the firm is worth more than the bonds, equity
  gets the difference.
• Just like a call option.

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Value of a Call Option before the Expiration Date
This is about the value of equity of a
nearly bankrupt firm.
Value to Equity
Higher risk implies higher value
Value of the physical firm ()
0
50
Bonds owed
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Risk

• Raises the value of the near bankrupt firm.
• Raises the value of a call option.

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The option to expand

• Project A restaurant with two locations.
• Probability .5 of modest success. NPV calculation
  holds.
• Probability .5 of huge success, expand to 100
  locations, capture value, become rich.
• Project is a call option in addition to having
  NPV.
• Option value can overcome conventional NPV lt 0.

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Definition of a put option

• A call option is the right but not the obligation
  to sell 100 shares of the stock at a stated
  exercise price on or before a stated expiration
  date.
• The premium (market price) of the option is not
  the exercise price.

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The option to abandon is a put.

• Project build and market a new surf board line.
  NPV over a long horizon.
• Probability .5 of success.
• Probability .5 of failure, which will be evident
  at once. Sell the machinery, cease operations.
• Value of put is in addition to usual NPV.

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Exam review

• AOL is considering building a cafeteria for its
  employees.
• At a high discount rate appropriate to AOLs
  risk, the NPV of the cafeteria is negative.
• At a low discount rate appropriate to a Wendys,
  the NPV of the cafeteria is positive.
• Should AOL build the cafeteria?
• Explain briefly.

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Answer

• Build the cafeteria.
• The project is safe like a Wendys, not risky
  like an internet service.
• NPV is market value.
• The market is not deceived but sees the project
  for the safe investment that it is.

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Sets of Information relevant to a stock
All information
Publicly availableinformation
Past prices
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Exam prep item

• What are the flaws of payback period as a measure
  of a projects worth?

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Answer

• In mutually exclusive choices, it ignores the
  effect of scale. It can incorrectly favor melons
  over malls.
• It doesnt adjust to changes in market interest
  rates.
• It ignores timing of cash flows inside the
  payback period.
• It ignores all cash flows after payback is
  complete.

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Exam review question

• When a firm creates value through a financial
  transaction, who gets the increase?

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Answer

• Old equity means the shareholders at the time the
  decision is made.
• Old equity gets the gains.
• Why? Old equity has no competitors. Everyone
  else is competitive and must accept a market
  return.
• Recall the first problem set.

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Exam prep item

• Two assets have the same expected return.
• Each has a standard deviation of 2.
• The correlation coefficient is .5.
• What is the standard deviation of an equally
  weighted portfolio?

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Answer

• Var P .5x.5x4.5x.5x42x.5x.5x.5x2x2
• 3
• Standard deviation sq. root of 3
• 1.732

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Exam prep

• A firm has a project with positive NPV.
• The project costs 100M to start.
• The firm has only 50M.
• What should it do?

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Answer

• Raise the money in the capital market.
• It can because NPV is market valuation.

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Exam prep item

• What is the weighted average cost of capital?

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Answer

• Dont tell us a story.
• Give the definitions and the formula.
• rB bond rate
• rS expected return on shares
• B market value of bonds
• S market value of shares
• TC corporate tax rate

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Pay-off pitch

• rWACC (S/(SB))rS (B/(SB))(1-TC)rB
• Now say that it applies when
• (1) the physical project has the same risk as the
  firm
• (2) it is financed like the firm.

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Exam review

• Does a good project have IRR greater than the
  hurdle rate, or less?

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Answer

• IRR is the discount rate that makes NPV(IRR) 0.
• The hurdle rate is the market rate for the
  risk-class.
• Investing means cash flows are first negative,
  then positive.
• Financing (in this context) means cash flows are
  first positive, then negative.

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More answer

• Other sign patterns, IRR is not useful.
• Investing, a good project has IRR gt hurdle rate.
• Financing, a good project has hurdle rate gt IRR.

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