Finance: risk neutral probabilities, and value of equity

Review Questions. 10-2 and 10-3 (attached)

----------------

Given
Available gas (MCF) 50,000,000
Price of Gas (today) $14.03 per MCF
Gas Price Next Year
High $18.16
Low $12.17
Forward price for next year $14.87
Development cost per MCF $4.00
Debt (on the property) $450,000,000
Interest rate on debt 10%
Debt maturity 1 year
Asking price for Equity $50,000,000
Risk free rate of interest 6.0%
Income tax rate 0.0%
Option Exercise price/MCF $13.90

Solution
a. Hedging (with futures) analysis
Revenue (hedged)
Less: Development cost
Less: Interest expense
EBT
Less: Taxes
Net Income

Less: Principal Payment $(450,000,000)
EFCF

Estimated value of the equity

b. Real Option analysis
High Price for Gas Low Price for Gas
Revenue (Not hedged)
Less: Development cost
Less: Interest expense
EBT
Less: Taxes
Net Income
Less: Principal Payment $(450,000,000) $(450,000,000)
EFCF

Calculating the risk neutral probabilities
Risk Neutral Pbs Option Payout Product
High price oil
Low price oil
Sum
Risk Neutral Expected EFCF
Equity Value

c. Valuing a Call Option on natural gas with an exercise price of 13.90 per MCF
Option Payouts Risk Neutral Pb Product
High price oil ($18.16/MCF)
Low price oil ($12.17/MCF)
Expected Payout
Call Value
Buy 50 m calls
-------------------------------------------

Given
Available oil (barrels) 20,000
Oil Price Next Year
High $50.00
Low $35.00
Forward price of oil for next year $40.00
Development cost $600,000.00
Extraction cost/barrel $8.00
Risk free rate of interest 5%
Income tax rate 0%

Solution
If the investment is hedged by selling the oil in the forward market
Revenue (hedged)
Less: Development cost (600,000)
Less: Extraction cost
EBT
Less: Taxes
Net Income

EFCF

Estimated value of the equity =

If the firm waits until the end of the year to decide whether to exercise the option to develop
Oil Price Scenario
High Low
Revenue (Not hedged)
Less: Development cost (600,000) (600,000)
Less: Extraction cost
EBT
Less: Taxes
Net Income

EFCF

Calculating the risk neutral probabilities
Risk Neutral Pbs Option Payout Product
High price oil
Low price oil
Sum
Risk Neutral Expected EFCF
Equity Value

-----------

PROBLEM 10-3

Strategy of shorting calls and going long on the project
Call strike price $13.90
Market (traded) price of call per MCF $1.86
Number of MCF $50,000,000.00

At time t = 0
Proceeds from shorting call
Investment in project (50,000,000.00)
Net proceeds at t = 0

At time t = 1
High Price Low Price
Gas price $18.16 $12.17
Payoffs on short call
Proceeds from project
Net proceeds at t = 1