Value maximization and options

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Value maximization and options

• Economics 234A

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Course web page (near future)

• www.econ.ucsb.edu/marshall

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If not already conversant with a spread sheet,
start immediately to learn.
Use it for problems 2, 3, 4, and 5.
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Key concepts of problem solving

• Equivalence (usually in present value,
  occasionally in rate of return)
• Optimization (choice of action)
• Aggregation (of values of cash flows)

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Webservice.com

• Example of valuation for a start-up
• Illustrates aggregation

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Key concepts

• Real investment
• Financial investment
• Separation principle

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Terminology

• Real investment buying physical capital
• Financial investment trading one asset for
  another
• e.g., money for shares of stock

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Principle of separation

• First value the real investment. (equivalence).
• Decide whether to undertake it (optimization).
• Then (separate decision) select the appropriate
  financial investment (optimization).

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Time zero is the present

• Time one is the future.
• Notation
• Cash flows at times zero, one

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Steps

• Status quo point (endowment point)
• Budget line
• Real investment.
• New budget line.

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equation of the budget constraint
Time one cash flow
status quo
Time zero cash flow
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Interest rate defined

• Premium for current delivery
• Duality of value and rate

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Interest rate defined

• Price of future money in terms of current money

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An investment opportunity that increases value.
Time one cash flow
Time zero cash flow
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Financial investments.
Time one cash flow
Time zero cash flow
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Financing possibilities, not physical investment
Time one cash flow
With- drawal
deposit
Time zero cash flow
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Separation application

• Modigliani-Miller
• Capital structure (financial investment)
• Dividends (financial investment)
• Shareholders wont pay the firm for doing what
  they can do themselves.
• Default analysis
• Not the last word

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Separation in broader context

• Intertemporal PPF
• General equilibrium at market prices, firms and
  consumers who optimize play their part in the
  overall efficient production and allocation of
  resources.

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Risk and value

• States of the world
• Visualize risk as branching.
• Chance points

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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 75.
• The call has an exercise price of 76.
• The value of the call seems to be zero.
• In fact, it is positive and in one example equal
  to 2.

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t 1
t 0
S 75
Value of call .5 x 4 2
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Definition of a put option

• A put 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 price of the option is not the exercise price.

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Example

• A share of IBM sells for 75.
• The put has an exercise price of 76.
• The value of the put seems to be 1.
• In fact, it is more than 1 and in our example
  equal to 3.

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Put-call parity

• S P Xexp(-r(T-t)) C at any time t.
• s p x c at expiration

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Options are financial investments

• Different iso-value line.
• In our example, the guy who owns a share of IBM
  can fully insure by buying 1.666 puts.
• Cost is 1.666 x 3 5. Net in the good state is
  80 5 75.
• Payoff in the bad state is 1.666 x 6 10
• Net in the bad state is 75 70 5 10.
• The position is riskless.

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Review question

• A standard question for midterm or final
  Suppose the owner of a firm has a good investment
  opportunity that uses all of her cash. She wants
  to consume right away. Which should she do?
  Explain.
• Answer do both.

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