Fill out all answer spaces in attached speadsheet

11-3 THE LOGIC OF HEDGING WITH OPTIONS Morrison Oil and Gas Company?s (from

Problem 11-1) chief financial analyst is Samuel (Sam) Crawford. Sam completed his

analysis, suggesting that the investment is indeed a good one for the company, and

presented it to the firm?s executive committee. The executive committee consists of

the firm?s CEO, CFO, and COO. The CFO thought Sam?s analysis was on target, but

the COO and CEO were concerned about the fact that the hedging strategy would not

work for the investment. In fact, they wondered why hedging the investment is such a

good idea. Sam thought for a second or two before responding and decided how to

best explain why the project is a good one and involves hedging the investment cash

flows using one-year call options on natural gas. These call options, which have a

$13.90-per-MCF strike price, are selling for $1.86 per MCF. Show how selling call

options on 50 MCF of gas today and undertaking the investment provides Morrison

with a hedged (i.e., risk-free) investment.

Titman, Sheridan; Martin, John D. (2014-04-08). Valuation (2nd Edition) (Prentice Hall Series in Finance) (Page 423). Prentice Hall. Kindle Edition.

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) $ (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., 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% = 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 Copper Price/Ton per Ton $ 7,000 $ 7,000 7,150 7,840 7,200 8,781 7,300 9,834 7,450 11,015 Forward Price Curve 2011 2012 2013 2014 2015 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 $ 7,000 7,150 7,200 7,300 7,450 Expected Price $ 7,000 7,840 8,781 9,834 11,015 Gain (loss) on FOR 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 $ $ $ 450,000 1,000,000 6 0.33 5 200,000 600 592.80 67.50 30.0% 5.0% 10.5% 7.0% 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 units pounds ounce per ton years units per ounce 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