Deck 17: Real Options

Question 1

Why is the perpetual call formula used to price commodity extraction options?

Answer 1

First,the option is a call since we have the right to invest.Second,the option,in theory,never expires and can be exercised early,thus,the perpetual call.

Question 2

Walla,Inc.may invest $6 million in a Buffalo harvesting project.Annual costs and revenues,starting next year,are forecasted to be $1 million and $0.7 million,growing at 0.0% and 3.0%,respectively.If the opportunity cost of capital is 4.5%,what is the investment trigger price?

A) $19.25 million
B) $21.25 million
C) $23.25 million
D) $25.25 million

Answer 2

C

Question 3

The price of oil is $115 per barrel.The effective lease rate and risk free rate are 3.0% and 4.0%,respectively.The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%.If an untapped well costs $2,100 to open and can produce indefinitely,what is the value of the unopened well?

A) $724
B) $854
C) $913
D) $1,025

Answer 3

C

Question 4

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

Question 5

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

Question 6

In the context of peak-load energy generation and a European exchange option,what is the spark spread?

Question 7

Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash flows with a binomial period of 1.Assume the initial cash flow (CF₁)is $20 million,σ = 0.45,r = 0.13,g = 0.02,and the project lasts 2 years.What is the value of the project on the up node in year 1?

A) $85 million
B) $185 million
C) $285 million
D) $385 million

Question 8

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

Question 9

The current price per ton of iron ore is $145.00.The effective lease rate is 3.0% and the risk free rate is 4.5%.The cost to mine one ton of iron ore is $110.00 and constant.What is the trigger price at which we will mine the iron ore?

A) $163.80
B) $180.40
C) $210.50
D) $205.70

Question 10

What is the relationship,in general,between volatility and trigger prices,assuming constant costs?

Question 11

The current price per cord of lumber is $26.00.The effective annual lease rate is 2.0% and the risk free rate is 4.0%.The cost to harvest one cord is $20.00 and constant.What is the trigger price at which we will harvest the lumber?

A) $27.61
B) $31.61
C) $35.61
D) $39.61

Question 12

The current price of silver is $ 31.00 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 silver is a constant $25.00,what is the value of an option to wait and mine the silver later?

A) $13.50
B) $14.50
C) $15.50
D) $16.50

Question 13

Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash flows with a binomial period of 1.Assume the initial cash flow is (CF₁)= $62 million,σ = 0.20,?rp = 0.14,and g = 0.03.What is the highest possible value of the project?

A) $222 million
B) $314 million
C) $622 million
D) $841 million

Question 14

The price of oil is $120 per barrel.The effective lease rate and risk free rate are 5.0% and 6.0%,respectively.The constant cost of extraction is $105 per barrel and the volatility of prices is 18.0%.What is the value of an option to defer extraction?

A) $30.68
B) $32.08
C) $34.56
D) $38.34

Question 15

What is the main difference in pricing R & D options versus most other real options?

Question 16

An existing well is operating and the price of oil is $115 per barrel.The effective lease rate and risk free rate are 3.0% and 4.0%,respectively.The constant cost of extraction is $85 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) $41
B) $48
C) $52
D) $59

Question 17

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

Question 18

Geek Is Us,Inc.may invest $8 million in an Alien Spectograph project.Annual costs and revenues,starting next year,are forecasted to be $3 million and $2 million growing at 0.0% and 4.0%,respectively.If the opportunity cost of capital is 6.0% and σ = 0.0,what is the investment trigger price?

A) $20.95 million
B) $30.95 million
C) $40.95 million
D) $50.95 million

Question 19

The price of oil is $115 per barrel.The effective lease rate and risk free rate are 3.0% and 4.0%,respectively.The constant cost of extraction is $85 per barrel and the volatility of prices is 15.0%.If an untapped well costs $2,100 to open and can produce indefinitely,at what price per barrel should the well be opened?

A) $349
B) $423
C) $454
D) $484

Question 20

The current price of silver is $32.00 per ounce.The effective lease rate and risk free rate are 3.0% and 4.0%,respectively.If the cost to mine one ounce of silver is a constant $25.00,what is the trigger price per ounce at which the silver will be mined?

A) $33.17
B) $35.17
C) $37.17
D) $39.17

Question 21

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.

Question 22

What two components go into valuing an infinite commodity reserve?