C16 Real Options II

Question 1

Risk-neutrality and financial assets’ cost of capital

Answer 1

If all market participants are risk neutral, then all financial assets (including options) have the same cost of capital, the the risk-free interest rate.

Question 2

Risk-neutral two-state model: formula stock-price and risk-neutral probability

Answer 2

S0 = [Su

Question 3

formula PV(call option) using risk-neutral probabilities

Answer 3

C0 = [

Question 4

Growth options: formula NPV of investing today

Answer 4

NPV = PV(Ann) - Investment0

Question 5

Growth options: finding risk-neutral probabilities

Answer 5

Problem: rf may either rise or fall and thus change NPV0. For finding risk-neutral probabilities, use T-year risk-free annuity
(1) PV(Ann.) S0 = C x [1-(1+rf)-T/ rf]
(2) Su = C + C x [1-(1+rf,u)-T/ rf,u]
(3) Sd = C + C x [1-(1+rf,d)-T/ rf,d]
(4)

Question 6

Option to abandon

Answer 6

Option value = NPV with option — NPV without option
Remark: If the cash flows are perpetual, NPVwithout option = CF / rf

Question 7

Two key insights from Real Options

Answer 7

1) Delay investment expenses as much as possible:
committing capital before it is absolutely necessary gives up the option to make a better decision once uncertainty is resolved
2) Create value by exploiting real options:
firm must continually re-evaluate its investment opportunities, including the options to delay or abandon projects, as well as to create or grow them