The Pampa Oil Company operates oil and gas exploration throughout the panhandle of Texas. The firm recently was approached by a wildcatter named William ?Wild Bill? Donovan with the prospect to develop what he thought was a sure thing. Wild Bill owned the lease and wanted to sell it to Pampa to meet some other pressing gambling debts. The exploration would involve efforts expended over the period of one year and cost $600,000 (which for simplicity we assume is paid at the end of the year). Wild Bill is extremely confident that there are 20,000 barrels of oil to be found, and he has engineering and geological reports to support his view. The value of the proposition hinges on the price of oil, the cost of exploration, and the cost of extracting the oil. Pampa Oil is very familiar with exploration and production in the area and is confident about its cost estimates. Pampa Oil estimates that the exploration would involve efforts expended over the period of six months and cost $600,000 (which for simplicity we assume is paid at the end of the year). Pampa oil also feels confident that the cost of extracting oil will be no more than $8 a barrel. However, oil prices have been very volatile, and the experts in the economy predict that oil prices might hit $50 a barrel by year-end or drop back to $35 depending upon progress made in securing a lasting peace in the Middle East. Pampa Oil is, therefore, considering the possibility of deferring development of the oil field for six months. Waiting for six months will place Pampa Oil in a better position to determine whether to go ahead with exploration or not. The risk-free rate of interest is currently 5%, and the forward price of oil one year in the future is now trading at $40 a barrel, what should the investment proposal be worth to Pampa (you may assume a zero income tax rate)

PROBLEM 11-1 Given Available gas (MCF) Price of Gas (today) Gas Price Next Year High Low Forward price for next year Development cost per MCF Debt (on the property) Interest rate on debt Debt maturity Asking price for Equity Risk free rate of interest Income tax rate Option Exercise price/MCF Solution Legend 50,000,000 $14.03 per MCF = Value given in problem = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output $18.16 $12.17 $14.87 $4.00 $450,000,000 10% 1 year $50,000,000 6.0% 0.0% $13.90 Solution a. Hedging (with futures) analysis Revenue (hedged) Less: Development cost Less: Interest expense EBT Less: Taxes Net Income Less: Principal Payment Equity FCF $(450,000,000) Present value of expected Equity FCF for year 1 where gas revenues are sold forward (hedged). Discounted at the risk free rate. Estimated value of the equity b. Real Option analysis High Price for Gas Revenue (Not hedged) Less: Development cost Less: Interest expense EBT Less: Taxes Net Income Less: Principal Payment Equity FCF Low Price for Gas Use forward price to calculate the risk neutral probability, i.e., $(450,000,000) Low Forward Price Price Low Probabilit y High Price Price Risk Neutral $(450,000,000) Calculating the risk neutral probabilities Risk Neutral Pbs Option Payout Product High price oil Low price oil Sum Risk Neutral Expected Equity FCF Equity Value c. Valuing a Call Option on natural gas with an exercise price of 13.90 per MCF Option Payouts Risk Neutral Pb High price oil ($18.16/MCF) Low price oil ($12.17/MCF) Expected Payout Call Value Buy 50 m calls Product The option to produce only when conditions are favorable is obviously valuable. It doubles the value of the equity in the gas venture. PROBLEM 11-2 Given Available oil (barrels) Oil Price Next Year High Low Forward price of oil for next year Development cost Extraction cost/barrel Risk free rate of interest Income tax rate Solution Legend 20,000 = Value given in problem = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output $50.00 $35.00 $40.00 $600,000.00 $8.00 5% 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 Equity FCF 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 Equity FCF Calculating the risk neutral probabilities Risk Neutral Pbs High price oil Low price oil Option Payout Sum Risk Neutral Expected Equity FCF Equity Value Product Present value of expected Equity FCF for year 1 where oil revenues are sold forward (hedged). Discounted at the risk free rate. Use forward price to calculate the risk neutral probability, i.e., Low Forward Risk Neutral Price Price Probabilit y Low High Price Price PROBLEM 11-3 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 Net proceeds at t = 0 Gas price Payoffs on short call Proceeds from project Net proceeds at t = 1 Solution Legend = Value given in problem = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output (50,000,000.00) At time t = 1 High Price $18.16 Low Price $12.17 You make $43,000,000 at t = 0 and there are no cash obligations next period. The strategy of investing in the project and shorting calls results in sure profits of $43 million today. PROBLEM 11-4 Given Initial investment Total Ore Quantity % Pure Copper/ton Life of project Ore mined each year Cost/ton for processing Tax rate Risk free rate WACC Growth in copper prices Solution Legend $60,000,000 75,000 tons 15% 5 years 15,000 tons $150.00 30% 5.5% 9.5% 12% Forward Price Curve 2011 2012 2013 2014 2015 Copper Price/Ton $7,000 7,150 7,200 7,300 7,450 = Value given in problem = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output Expected Prices per Ton $7,000 7,840 8,781 9,834 11,015 Solution a. Revenues Processing Costs Depreciation/ Depletion NOI NOPAT Plus: Depreciation Project FCF Revenues Year 2011 2012 2013 2014 2015 Processing Costs Depreciation/ Depletion NOI NOPAT Plus: Depreciation Project FCF Bond Payoffs Total payoffs b. NPV c. Year 2011 2012 2013 2014 2015 NPV Tracking portfolio Year 2011 2012 2013 2014 2015 Cost at t = 0 Total cost (Track. Port) Cost of investment Savings Forward price Expected Price Gain (loss) on FOR $7,000 $7,000 7,150 7,840 7,200 8,781 7,300 9,834 7,450 11,015 PROBLEM 11-5 Given Risk free rate Spot price (gold) Number of ounces Cost of 175 ounces Maturity Forward price (175 ounces) Solution Legend 5.00% $571.43 175 $100,000.00 1 $104,000.00 = Value given in problem = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output Solution Strategy of Client (Short gold today, invest in treasury and go long on forward contract) TODAY Short gold (175 ounces) Invest treasury (@ 5%) Long forward (@104,000) Net Cash Flow NEXT YEAR $100,000.00 Cover short position $(100,000.00) Treasury bill payoff 0 Close forward $Net Cash Flow -P Jim Lytle Strategy (Buy 175 ounces of gold today and sell next year) TODAY Buy gold (175 ounces) Borrow 100,000 Net Cash Flow NEXT YEAR $(100,000.00) Sell gold at P $100,000.00 Repay risk free loan $Net Cash flow P P is the REALIZED price of 175 ounce of gold next year If the price of 175 ounces of gold goes above $106,000, Jim Lytle's strategy pays off more than the client's strategy. On the other hand if the price of 175 ounces of gold stays below $106,000, the client's strategy provides greater payoffs. PROBLEM 11-6 Given Initial investment Total PCs scrapped Electronic scrap per PC Gold content Life of project PCs scrapped per year Tons of scrap per year Current price of gold Cost/ton for processing Tax rate Risk free rate WACC Growth in gold prices Forward Price Curve 2011 2012 2013 2014 2015 Solution Legend $450,000 1,000,000 units 6 pounds 0.33 ounce per ton 5 years 200,000 units 600 $592.80 per ounce $67.50 30.0% 5.0% 10.5% 7.0% = Value given in problem = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output Gold Expected Prices Price/Ounce per Ounce $679.40 $634.30 715.10 678.70 750.60 726.21 786.90 777.04 822.80 831.43 Solution a. Revenues Processing Costs Depreciation/ Depletion NOI NOPAT Plus: Depreciation Project FCF Revenues Year 2011 2012 2013 2014 2015 Processing Costs Depreciation/ Depletion NOI NOPAT Plus: Depreciation Project FCF Processing Costs Depreciation/ Depletion NOI NOPAT Plus: Depreciation b. NPV c. Year 2011 2012 2013 2014 2015 NPV To solve for equivalent growth rate, use the following: Year 2011 2012 2013 2014 2015 Expected Price Revenues NPV Difference Use Solver. Set difference to zero by changing growth rate cell (yellow highlighted) Project FCF