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Fundamentals of Derivatives Markets (McDonald)
Chapter 14 Real Options
14.1 Multiple Choice Questions
When answering the questions below, refer to the following table and related data.
Project Cash Flow Tree From a New Project
Year 1 Year 2 Year 3
120.52 155.67 222.64
65.24 84.27 120.52
45.62 65.24
35.32
Effective annual risk free rate = 4.5%
Expected market return = 10%
Cash flow beta = 1.4
The true probability of the high cash flow in a given period is 52.0%.
1) What is the risk neutral probability of an upward movement in the project cash flows during
the first year of operations?
A) 35.6%
B) 40.3%
C) 48.1%
D) 59.7%
2) What is the risk neutral probability of the first two years of the project cash flows moving
down?
A) 40.3%
B) 48.0%
C) 52.0%
D) 59.7%
3) If the project has an $80 annual cost requirement, what is the first year risk neutral expected
cash flow?
A) $93.99
B) $87.54
C) $13.99
D) $7.54
4) If we continue to consider the $80 annual cost, but are able to avoid operating in years where
money will be lost, what is the expected risk neutral cash flow in year 2?
A) $2.12
B) $14.36
C) $80.00
D) $82.12
5) What is the value of the project if the true probabilities are used and the appropriate one
period risk adjusted discount rate is used (assume the $80 annual cost does not exist)?
A) $169.65
B) $201.42
C) $233.73
D) $288.64
6) What is the value of the project assuming an $80 annual cost?
A) $10.86
B) $13.81
C) $33.52
D) $47.33
7) What is the value of the project assuming an $80 annual cost and the option of not pursing
the project in periods where cash flow is negative?
A) $10.86
B) $13.81
C) $33.52
D) $47.33
8) Given the requirement of an $80 annual cost, what is the value of the option to abandon the
project in periods where the cash flows are negative?
A) $10.86
B) $13.81
C) $33.52
D) $47.33
9) Given the requirement of an $80 annual expenditure, what is the elasticity of the cash flows
in period 1, with respect to the scenario in which no investment is required?
A) 1.40
B) 7.08
C) 9.68
D) 11.62
10) What is another term used to describe the forward price?
A) Certainty equivalent
B) Elasticity
C) Risk neutral price
D) Value
11) The phrase in real option theory used to replace the strike price?
A) Exercise
B) Investment
C) PV of asset
D) Trend
12) Mead, Inc. may invest $20 million in a new fiber optic project. Due to market conditions,
annual production costs and revenues are forecasted at $10 million and $8 million,
respectively, starting next year. Revenues are expected to grow at 4.0% and interest rates are
6.0%. What is the change in value if the project is commenced in 5 years instead of today?
(Use static analysis.)
A) $8.84 million
B) $10.84 million
C) $12.84 million
D) $14.84 million
13) Techie, Inc. may invest $5 million in a new Star Communicator project. Annual production
costs and revenues are projected to be $2 million and $1.5 million, with each growing at 2.0%
and 4.0%, respectively. At an interest rate of 5.5%, what is the approximate investment year
that will maximize value? (Use static analysis.)
A) Year 20
B) Year 15
C) Year 10
D) Year 5
14) Use a binomial tree to value the following option. Assume rf = 0.04, rp =0.12, σ = 0.35, E(CF1)
= $30, and cost = $300. What is the value of this project option?
A) $40.74
B) $50.60
C) $55.32
D) $62.12
15) Use a binomial tree to value to following option. Assume rf = 0.045, rp = 0.14, σ = 0.20, E(CF1)
= $62 million, g = 0.03, time horizon = 2 years, binomial period = 1 year, and cost = $500
million. What is the value of this project option?
A) $47 million
B) $57 million
C) $67 million
D) $77 million
16) The current price of gold is $310.00 per ounce. The effective lease rate and risk free rate are
1.0% and 3.5%, respectively. If the cost to mine one ounce of gold is a constant $250, what is
the value of an option to wait and mine the gold later?
A) $135
B) $145
C) $155
D) $165
17) The price of oil is $22 per barrel. The effective lease rate and risk free rate are 5.0% and 6.0%,
respectively. The constant cost of extraction is $18 per barrel and the volatility of prices is
18.0%. What is the value of an option to defer extraction?
A) $5.34
B) $6.34
C) $7.34
D) $8.34
18) The price of oil is $45 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%,
respectively. The constant cost of extraction is $25 per barrel and the volatility of prices is
15.0%. If an untapped well costs $240 to open and can produce indefinitely, what is the value
of the unopened well?
A) $424
B) $554
C) $635
D) $785
19) The price of oil is $45 per barrel. The effective lease rate and risk free rate are 3.0% and 4.0%,
respectively. The constant cost of extraction is $25 per barrel and the volatility of prices is
15.0%. If an untapped well costs $240 to open and can produce indefinitely, at what price per
barrel should the well be opened?
A) $34
B) $44
C) $54
D) $64
20) An existing well is operating and the price of oil is $45 per barrel. The effective lease rate and
risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction is $25 per barrel
and the volatility of prices is 15.0%. If it costs nothing to shut down the well, at what price
would we close the well?
A) $12
B) $25
C) $37
D) $49
14.2 Short Answer Essay Questions
1) Why is the Black Scholes formula not viable when pricing a spread option for electricity?
2) Why is the perpetual call formula used to price commodity extraction options?
3) What is the main difference in pricing R & D options versus most other real options?
5
4) In the context of peak-load energy generation and a European exchange option, what is the
spark spread?
5) What feature of the abandonment option makes the use binomial pricing more appealing
than the Black Scholes pricing model?
14.3 Class Discussion Question
1) How are call and put options used to value starting, stopping, and restarting commodity
extraction projects? Ask students to identify the calls and puts in each situation.
