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 one is the future. Notation:

Cash flows at times zero, one

Time zero is the present

10 ,cc

Steps

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

0c

1c

= status quo),( 10 cc

Time zero cash flow

Timeonecashflow

equation of the budgetconstraint:

11001100 cpcpcpcp

)1(1

0 rp

pslope

Interest rate defined

Premium for current delivery

Duality of value and rate

11

0 p

pr

Interest rate defined

Price of future money in terms of current money

0

1

1

1

p

p

r

0c

1c

),( 10 cc

Time zero cash flow

Timeonecashflow

An investment opportunity that increases value.

NPV

0c

1c

),( 10 cc

Time zero cash flow

Timeonecashflow

Financial investments.

NPV

0c

1c

),( 10 cc

Time zero cash flow

Timeonecashflow

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 = 0Pr. = .5

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 – 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.