Transcript Value maximization and options Economics 234A

Value maximization and options
Economics 234A
Course web page (near future)
 www.econ.ucsb.edu/~marshall
If not already conversant with
a spread sheet, start
immediately to learn.
Use it for problems 2, 3, 4, and 5.
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)
Webservice.com
 Example
of valuation for a start-up
 Illustrates aggregation
Key concepts
 Real
investment
 Financial investment
 Separation principle
Terminology
 Real
investment = buying physical
capital
 Financial investment = trading one
asset for another
e.g.,
money for shares of stock
Principle of separation
 First
value the real investment.
(equivalence).
 Decide whether to undertake it
(optimization).
 Then (separate decision) select the
appropriate financial investment
(optimization).
Time zero is the present
 Time
one is the future.
 Notation:
c0 ,c1
 Cash
flows at times zero, one
Steps
 Status
quo point (endowment point)
 Budget line
 Real investment.
 New budget line.
equation of the budget
constraint:
c1
p0c0  p1c1  p0 c0  p1 c1
p0
slope  
 (1  r )
p1
(c0 , c1 ) = status quo
c0
Time zero cash flow
Interest rate defined
 Premium
for current delivery
p0
r
1
p1
 Duality
of value and rate
Interest rate defined
 Price
of future money in terms of
current money
1
p1

1  r p0
c1
An investment opportunity
that increases value.
(c0 , c1 )
Time zero cash flow
NPV
c0
c1
Financial investments.
(c0 , c1 )
Time zero cash flow
NPV
c0
Financing possibilities,
not physical investment
c1
Withdrawal
(c0 , c1 )
deposit
c0
Time zero cash flow
Separation application
 Modigliani-Miller
 Capital
structure (financial investment)
 Dividends (financial investment)
 Shareholders won’t pay the firm for
doing what they can do themselves.
 Default analysis
 Not the last word
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.
Risk and value
 States
of the world
 Visualize risk as branching.
 Chance points
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.
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.
t=0
t=1
S = 80, call = 4
S = 75
S = 70, call = 0
Value of call = .5 x 4 = 2
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.
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.
Put-call parity
S
+ P = X*exp(-r(T-t)) + C at any time t.
 s + p = x + c at expiration
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.
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.