12/10/2012
REAL OPTIONS: THE INVESTMENT TIMING OPTION
Cost= ($70)
WACC= 10%
Risk-free rate= 6%
Demand Prob.
Annual
Cash Flow
Prob. x
(CF)
High 0.3 $45 $13.50
Procedure 1: DCF Only
Year 1 2 3
Expected CF $30.00 $30.00 $30.00
NPV= $4.61
Procedure 3: Decision Tree Analysis
a. Scenario Analysis: Proceed with Project Today
Cost NPV this Prob. Data for
Year 0 Prob. 1 2 3 Scenario x NPV
$45 $45 $45 $41.91 $12.57 417
b. Decision Tree Analysis: Implement in One Year Only if Optimal
Cost NPV this Prob. Data for
Year 0 Prob. 12 3 4
Scenarioax NPV
Chapter 26. Real Options
Future Cash Flows
Future Cash Flows
Std Deviation
a. What are some types of real options? Answer: See Chapter 26 Mini Case Show
b. What are the five steps for analyzing a real option? Answer: See Chapter 26 Mini Case Show
c. Tropical Sweets is considering a project that will cost $70 million and will generate expected cash
flows of $30 per year for three years. The cost of capital for this type of project is 10 percent and the
risk-free rate is 6 percent. After discussions with the marketing department, you learn that there is a 30
percent chance of high demand, with future cash flows of $45 million per year. There is a 40 percent
chance of average demand, with cash flows of $30 million per year. If demand is low (a 30 percent
chance), cash flows will be only $15 per year. What is the expected NPV?
Std Deviation
cost will still be $70 million at the end of the year, and the cash flows for the scenarios will still last
three years. However, Tropical Sweets will know the level of demand, and will implement the project
only if it adds value to the company. Perform a qualitative assessment of the investment timing
d. Now suppose this project has an investment timing option, since it can be delayed for a year. The
Assume that you have just been hired as a financial analyst by Tropical Sweets Inc., a mid-sized
California company that specializes in creating exotic candies from tropical fruits such as mangoes,
papayas, and dates. The firm’s CEO, George Yamaguchi, recently returned from an industry corporate
executive conference in San Francisco, and one of the sessions he attended was on real options.
Since no one at Tropical Sweets is familiar with the basics of real options, Yamaguchi has asked you to
prepare a brief report that the firm’s executives could use to gain at least a cursory understanding of
the topics.
e. Use decision tree analysis to calculate the NPV of the project with the investment timing option.
$0 $0 $0 $0 $0.00 $0.00 39
Notes:
Procedure 4: Analysis with a Financial Option
Find the Year 1 Value and Risk of Future Cash Flows If Project is Deferred
PV at Prob. Data for
Year 0 Prob. 1 2 3 4 Year 1 x Value
$45 $45 $45 $111.91 $33.57 417
30%
Find the current value of future cash flows if project is deferred (note: this is the estimate of P).
Current Value = Year 1 Value = $74.61 = $67.82
(1+WACC) 1.10
Use the direct approach to estimate the variance of the project’s rate of return.
Probability Data for
PVYear 0 PVYear 1 Return
Probability
$111.91 65.00% 0.30 19.5% 9.1%
return; to find the value of this real option, we need the standard deviation of the projects expected rate
of return.
The option to defer the project is like a call option. The company has until Year 1 to decide whether or
not to implement the project, so the time to maturity of the option is one year. If the company exercises
the option, it must pay a strike price equal to the cost of implementing the project. If the company does
The first step is to find the value of the project’s future cash flows, as of the time the option must be
exercised. We also need the standard deviation of the project’s value as of the date it must be
exercised. Finally, we need the present value of the project’s future cash flows.
Std Deviation
Use the indirect approach to estimate the variance of the project’s rate of return. Start by estimating the
coefficient of variation, CV, of the project’s value at the time the option expires. This was done in an earlier
step.
Std Deviation
f. Use a financial option pricing model to estimate the value of the investment timing option.
Future Cash Flows
x ReturnYear 1
CV =Coefficient of Variation = 0.39
Now use the following formula to estimate the variance of the project’s rate of return.
Find the Value of a Call Option Using the Black-Scholes Model
Real Option
rRF = 6%
t = 1
X = $70.00
P = $67.82
s2 = 14.2%
REAL OPTIONS: THE GROWTH OPTION
Original Project
Cost NPV this Prob. Data for
Year 0 Prob. 1 2 3 Scenario x NPV
$45 $45 $45 $36.91 $11.07 417.45
NPV without growth option:
NPV = -$0.39
NPV = -$0.39 + -$0.30
NPV = -$0.69
Expected NPV is you simply repeat project at time 3:
NPV = NPV of project 1 + PV of repeated project
Decision Tree: Implement the repeated project only if demand is high. Data for
h. Tropical Sweets will replicate the original project only if demand is high. Using decision tree
analysis, estimate the value of the project with the growth option.
g. Now suppose the cost of the project is $75 million and the project cannot be delayed. But if Tropical
Sweets implements the project, then Tropical Sweets will have a growth option. It will have the opportunity
to replicate the original project at the end of its life. What is total expected NPV of the two projects if both
are implemented?
Std Deviation
Financial Option
Future Cash Flows
t
]1CVln[ 2
2+
=s
Cost NPV this Prob. Std Deviation
Year 0 Prob. 1 2 3 4 5 6 Scenario x NPV
$45 $45 -$30 $45 $45 $45 $58.02 $17.40 1,010
Notes: 1. The CF in Year 3 includes the cost to implement the second project if it is optimal to do so.
Financial Option Approach
Find the value and risk of the future cash flows as of the time the option expires. Data for
Cost PV at Prob. Std Deviation
Year 0 Prob. 1 2 3 4 5 6 Year 3 x NPV
$45 $45 $45 $111.91 $33.57 417
30%
Find the current value of future cash flows if project is deferred (note: this is the estimate of P).
Current Value = Year 3 Value = $74.61 = $56.05
(1+WACC)31.33
P = $56.05
Use the direct approach to estimate the variance of the project’s rate of return.
Annual Data for
PVYear 0 1 2 PVYear 3 Return
Probability
x Return2005
Std Deviation
$111.91 25.9% 0.30 7.8% 1.0%
CV =Coefficient of Variation = 0.39
Now use the following formula to estimate the variance of the project’s rate of return.
Use the indirect approach to estimate the variance of the project’s rate of return. Start by estimating the
coefficient of variation, CV, of the project’s value at the time the option expires. This was done in an earlier
step.
i. Use a financial option model to estimate the value of the growth option.
2. When finding the NPV, the cost to implement the second project is discounted at the risk-free rate;
other cash flows are discounted at the cost of capital.
Future Cash Flows
Future Cash Flows
t
]1CVln[ 2
2+
=s
Find the Value of a Call Option Using the Black-Scholes Model
Sensitivity Analysis
Base Case Case 1 Case 2
rRF = 6% 6% 6%
t = 3 3 3
j. What happens to the value of the growth option if the variance of the project’s return is 14.2 percent?
What if it is 50 percent? How might this explain the high valuations of many dot.com companies?