Problems

Skill-Building Problems.

1. You have the opportunity to purchase a piece of land for $0.7 million which has known reserves

of 375,000 barrels of oil. The reserves are worth $12.6 million based on the current crude oil

price of $33.60 per barrel. The cost of building the plant and equipment to develop the oil is $4.5

million, so it is not profitable to develop these reserves right now. However, development may

become profitable in the future if the price of crude oil goes up. For simplicity, assume there is a

single date in 1.4 years when you can decide whether to develop the oil or not. Further assume

that all of the oil can be produced immediately. Using historical data on crude oil prices, you

determine that the mean value of the reserves is $13.4 million based on a mean value of the oneyear

ahead oil price of $35.73 per barrel and the standard deviation 30.0%. The riskfree rate is

4.7% and cost of capital for a project of this type is 12.15%. What is the project’s NPV using the

Black-Scholes call formula? What would the NPV be if you committed to develop it today no

matter what and thus, (incorrectly) ignored the option to develop the oil only if it is profitable?

2. Given the same real options project as problem 1, calculate the project’s NPV using the binomial

model. Compare this result to the Black-Scholes result.

3. What would happen if you increased asset value standard deviation to the NPV Using Black-

Scholes, NPV Ignoring Option, and NPV Using Binomial?

Live In-class Problems.

4. Given the partial Using Black Scholes spreadsheet RealoblZ.xls, do steps 2 NPV using Black-

Scholes, 3 Expected Cash Flows, 4 Present Value of Expected Cash Flows, and 5 NPV

Ignoring Option.

5. Given the partial Using The Binomial Model spreadsheet RealoblZ.xls, do step 5 NPV using

Binomial.

6. Given the partial Sensitivity to Std Dev spreadsheet RealostZ.xls, do steps 2 Create A List of

Input Values, Two Output Formulas, And A Standard Deviation Connection and 3 Data

Table.

Skill-Building Problems.

1. You have the opportunity to purchase a piece of land for $0.7 million which has known reserves

of 375,000 barrels of oil. The reserves are worth $12.6 million based on the current crude oil

price of $33.60 per barrel. The cost of building the plant and equipment to develop the oil is $4.5

million, so it is not profitable to develop these reserves right now. However, development may

become profitable in the future if the price of crude oil goes up. For simplicity, assume there is a

single date in 1.4 years when you can decide whether to develop the oil or not. Further assume

that all of the oil can be produced immediately. Using historical data on crude oil prices, you

determine that the mean value of the reserves is $13.4 million based on a mean value of the oneyear

ahead oil price of $35.73 per barrel and the standard deviation 30.0%. The riskfree rate is

4.7% and cost of capital for a project of this type is 12.15%. What is the project’s NPV using the

Black-Scholes call formula? What would the NPV be if you committed to develop it today no

matter what and thus, (incorrectly) ignored the option to develop the oil only if it is profitable?

2. Given the same real options project as problem 1, calculate the project’s NPV using the binomial

model. Compare this result to the Black-Scholes result.

3. What would happen if you increased asset value standard deviation to the NPV Using Black-

Scholes, NPV Ignoring Option, and NPV Using Binomial?

Live In-class Problems.

4. Given the partial Using Black Scholes spreadsheet RealoblZ.xls, do steps 2 NPV using Black-

Scholes, 3 Expected Cash Flows, 4 Present Value of Expected Cash Flows, and 5 NPV

Ignoring Option.

5. Given the partial Using The Binomial Model spreadsheet RealoblZ.xls, do step 5 NPV using

Binomial.

6. Given the partial Sensitivity to Std Dev spreadsheet RealostZ.xls, do steps 2 Create A List of

Input Values, Two Output Formulas, And A Standard Deviation Connection and 3 Data

Table.