lecture 5: INVESTMENT IN REAL PROJECTS AND OPTIONS Flashcards
The firm’s ability to delay its investment and operating decisions until the release of information
we wait to make the investment decision because we do not have all the info yet
we have to consider all the possibilities we can face until we are sure for certain
basically, like a call option
a call option
gives its owner the fight to buy a fixed number of securities (e.g. shares) at a fixed price (exercises price) on or before a given date
we can pull out whenever we want
–> one should generally not exercise a call option immediately (like in the drilling example)
the serious deficiency in classical capital budgeting we see in this section
NPV calculations typically ignore the flexibility that real-world firms have
the fundamental weakness irreversibility of the NPV rule
Once a project is committed based on NPV evaluation, there is no recourse as abruptly stopping a project during implementation can be very costly and is almost impossible to have it reversed once project is complete
The NPV Rule anticipates no contingency for delaying a project or abandoning it if market conditions turn sour
The application of Option Theory in Capital Budgeting is particularly useful in which 3 situations?
this is what the NPv fails to consider
Possibility of delaying a project
Possibility of future expansion
Possibility of abandoning a project
The option
by definition is a choice, not an obligation
it is always advantageous to the holder of the option
a contract that gives its owner (holder) the right to buy or sell some assets (fixed assets*, securities, foreign exchanges) at a fixed price on or before a given date some time in the future
put option
gives owner right to sell at fixed price on or before given date
what do buyers of call options (holders) expect ?
expect share prices to go up (long position)
what do sellers of call options (writers) expect ?
expect share prices to go down (short position)
call option out-of-money
current stock price < strike price
call option at-of-money
current stock price = strike price
call option in-of-money
current stock price > strike price
black Scholes model
mathematical model for pricing an options contract
Black-Scholes Formula for call option excluding dividends
C = P · N(d1) - S · e^-(RF · t) · N(d2)
P: current stock price
S: Strike price of option
t: time to expiration in years
RF: risk free rate
N(d1) and (d2) are the things of risk
Black-Scholes Formula for call option with the dividend adjustment
call options become less valuable because stock price declines
C = P · e^-(Y · t) · N(d1) - S · e^-(RF · t) · N(d2)
P: current stock price
S: Strike price of option
t: time to expiration in years
RF: risk free rate
N(d1) and (d2) are the things of risk
N(d1) and (d2) formula for call option no dividend included
same as put option
d1 = (ln(P/S) + (RF + (σ^2)/2) · t) / σ · t^(1/2)
d2 = d1 - σ · t^(1/2)
N(d1) and (d2) formula for call option with dividend adjustment
d1 = (ln · (P/S) + (RF - Y + (σ^2)/2) · t) / σ · t^(1/2)
Y = dividend yield (dividend/current price)
d2 = d1 - σ · t^(1/2)
–> does not change
Black-Scholes Formula for put option
value of put = S · e^-(RF · t) · (1 - N(d2)) - P · e^-(RF · t) · (1- N(d1))
d1 and d2 are same as call option
option to delay a project
company receives exclusive rights to project
NPV = PV - C
C being the initial investment
invest if PV > C because NPV > 0
in the option to delay a project, what happens if PV < C?
the company already bought the exclusive rights
the only loss they will incur is the investment of securing the exclusive rights
how to apply the Black-Scholes method to a project with delay options
we first find the NPv
P = PV of future cash flows
S = initial investment of project
t = expiration of exclusive right
σ^2 = variance of the future cash flows
Y = cost of delaying the investment
this will give the value of the exclusive project
where do we usually find exclusive rights for projects
patents
old and gas drilling (natural resource development)
mines (mineral) (natural resource development)
land for future developments
what are the uncertainties when valuing natural resource investments as options?
available reserves of resources
initial cost to develop
variance in the underlying asset
cost of delay
option to expand
options to pave the way for other projects
–> can’t move forward if not investment is made on this initial project
firms may accept negative NPVs
kinda similar to call options
examples of options to expand
entry into large growing markets
technological expertise
brand name
research, development, and test markets
major problems when evaluation option to expand
lack of specific time horizon by which firms have to make an expansion decision (open-ended decision)
difficulty in determining the size and potential of such future markets
option to abandon a project
valuable when a project can bring about significant losses
how to calculate the value of an option to abandon a project
the same way as a put option
V = PV of remaining cash flows in the future
L = cost of abandonment or liquidation
n = remaining number of years in the project
if V > L, continue with the project
if V < L, abandon the project
