Value maximization and options Economics 234A

Course web page (near future) 

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 one is the future.  Notation:  Cash flows at times zero, one Time zero is the present

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

= status quo Time zero cash flow Time one cash flow equation of the budget constraint:

Interest rate defined  Premium for current delivery  Duality of value and rate

Interest rate defined  Price of future money in terms of current money

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

Time zero cash flow Time one cash flow Financial investments. NPV

Time zero cash flow Time one cash flow Financing possibilities, not physical investment deposit With- drawal

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 = 75 S = 80, call = 4 S = 70, call = 0 Pr. =.5 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 –  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.