lecture 5: INVESTMENT IN REAL PROJECTS AND OPTIONS

Question 1

The firm’s ability to delay its investment and operating decisions until the release of information

Answer 1

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

Question 2

a call option

Answer 2

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)

Question 3

the serious deficiency in classical capital budgeting we see in this section

Answer 3

NPV calculations typically ignore the flexibility that real-world firms have

Question 4

the fundamental weakness irreversibility of the NPV rule

Answer 4

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

Question 5

The application of Option Theory in Capital Budgeting is particularly useful in which 3 situations?

this is what the NPv fails to consider

Answer 5

Possibility of delaying a project

Possibility of future expansion

Possibility of abandoning a project

Question 6

The option

Answer 6

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

Question 7

put option

Answer 7

gives owner right to sell at fixed price on or before given date

Question 8

what do buyers of call options (holders) expect ?

Answer 8

expect share prices to go up (long position)

Question 9

what do sellers of call options (writers) expect ?

Answer 9

expect share prices to go down (short position)

Question 10

call option out-of-money

Answer 10

current stock price < strike price

Question 11

call option at-of-money

Answer 11

current stock price = strike price

Question 12

call option in-of-money

Answer 12

current stock price > strike price

Question 13

black Scholes model

Answer 13

mathematical model for pricing an options contract

Question 14

Black-Scholes Formula for call option excluding dividends

Answer 14

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

Question 15

Black-Scholes Formula for call option with the dividend adjustment

Answer 15

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

Question 16

N(d1) and (d2) formula for call option no dividend included

same as put option

Answer 16

d1 = (ln(P/S) + (RF + (σ^2)/2) · t) / σ · t^(1/2)

d2 = d1 - σ · t^(1/2)

Question 17

N(d1) and (d2) formula for call option with dividend adjustment

Answer 17

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

Question 18

Black-Scholes Formula for put option

Answer 18

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

Question 19

option to delay a project

Answer 19

company receives exclusive rights to project

NPV = PV - C

C being the initial investment

invest if PV > C because NPV > 0

Question 20

in the option to delay a project, what happens if PV < C?

Answer 20

the company already bought the exclusive rights

the only loss they will incur is the investment of securing the exclusive rights

Question 21

how to apply the Black-Scholes method to a project with delay options

Answer 21

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

Question 22

where do we usually find exclusive rights for projects

Answer 22

patents

old and gas drilling (natural resource development)

mines (mineral) (natural resource development)

land for future developments

Question 23

what are the uncertainties when valuing natural resource investments as options?

Answer 23

available reserves of resources

initial cost to develop

variance in the underlying asset

cost of delay

Question 24

option to expand

Answer 24

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

Question 25

examples of options to expand

Answer 25

entry into large growing markets

technological expertise

brand name

research, development, and test markets

Question 26

major problems when evaluation option to expand

Answer 26

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

Question 27

option to abandon a project

Answer 27

valuable when a project can bring about significant losses

Question 28

how to calculate the value of an option to abandon a project

Answer 28

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