# 11-3 THE LOGIC OF HEDGING WITH OPTIONS Morrison Oil and Gas Company’s (from Problem 11-1)

Fill out all answer spaces in attached speadsheet11-3 THE LOGIC OF HEDGING WITH OPTIONS Morrison Oil and Gas Company’s (fromProblem 11-1) chief financial analyst is Samuel (Sam) Crawford. Sam completed hisanalysis, suggesting that the investment is indeed a good one for the company, andpresented it to the firm’s executive committee. The executive committee consists ofthe firm’s CEO, CFO, and COO. The CFO thought Sam’s analysis was on target, butthe COO and CEO were concerned about the fact that the hedging strategy would notwork for the investment. In fact, they wondered why hedging the investment is such agood idea. Sam thought for a second or two before responding and decided how tobest explain why the project is a good one and involves hedging the investment cashflows 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 calloptions on 50 MCF of gas today and undertaking the investment provides Morrisonwith 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 11-1GivenAvailable gas (MCF)Price of Gas (today)Gas Price Next YearHighLowForward price for next yearDevelopment cost per MCFDebt (on the property)Interest rate on debtDebt maturityAsking price for EquityRisk free rate of interestIncome tax rateOption Exercise price/MCF$$$$$$$$Solution Legend50,000,00014.03 per MCF= Value given in problem= Formula/Calculation/Analysis required= Qualitative analysis or Short answer required= Goal Seek or Solver cell= Crystal Ball Input= Crystal Ball Output18.1612.1714.874.00450,000,00010%1 year50,000,0006.0%0.0%13.90Solutiona. Hedging (with futures) analysisRevenue (hedged)Less: Development costLess: Interest expenseEBTLess: TaxesNet IncomeLess: Principal PaymentEquity FCF$(450,000,000)Present value ofexpected EquityFCF for year 1where gas revenuesare sold forward(hedged).Discounted at therisk free rate.Estimated value of the equityb. Real Option analysisHigh Price for GasRevenue (Not hedged)Less: Development costLess: Interest expenseEBTLess: TaxesNet IncomeLess: Principal PaymentEquity FCFLow Price for GasUse forward price to calculate the risk neutralprobability, i.e.,$(450,000,000) $(450,000,000)Calculating the risk neutral probabilitiesRisk Neutral PbsOption PayoutProductHigh price oilLow price oilSumRisk Neutral Expected Equity FCFEquity Valuec. Valuing a Call Option on natural gas with an exercise price of 13.90 per MCFOption PayoutsRisk Neutral PbHigh price oil ($18.16/MCF)Low price oil ($12.17/MCF)Expected PayoutCall ValueBuy 50 m callsProductThe option toproduce only whenconditions arefavorable isobviously valuable.It doubles the valueof the equity in thegas venture.PROBLEM 11-2GivenAvailable oil (barrels)Oil Price Next YearHighLowForward price of oil for next yearDevelopment costExtraction cost/barrelRisk free rate of interestIncome tax rateSolution Legend20,000$$$$$= Value given in problem= Formula/Calculation/Analysis required= Qualitative analysis or Short answer required= Goal Seek or Solver cell= Crystal Ball Input= Crystal Ball Output50.0035.0040.00600,000.008.005%0%SolutionIf the investment is hedged by selling the oil in the forward marketRevenue (hedged)Less: Development cost(600,000)Less: Extraction costEBTLess: TaxesNet IncomeEquity FCFEstimated value of the equity =If the firm waits until the end of the year to decide whether to exercise the option to developOil Price ScenarioHighLowRevenue (Not hedged)Less: Development cost(600,000)(600,000)Less: Extraction costEBTLess: TaxesNet IncomeEquity FCFCalculating the risk neutral probabilitiesRisk Neutral PbsHigh price oilLow price oilOption PayoutSumRisk Neutral Expected Equity FCFEquity ValueProductPresent value ofexpected Equity FCF foryear 1 where oilrevenues are soldforward (hedged).Discounted at the riskfree rate.Use forward price to calculate the risk neutralprobability, i.e.,PROBLEM 11-3Strategy of shorting calls and going long on the projectCall strike price$13.90Market (traded) price of call per MCF$1.86Number of MCF$ 50,000,000.00At time t = 0Proceeds from shorting callInvestment in projectNet proceeds at t = 0Gas pricePayoffs on short callProceeds from projectNet proceeds at t = 1Solution Legend= Value given in problem= Formula/Calculation/Analysis required= Qualitative analysis or Short answer required= Goal Seek or Solver cell= Crystal Ball Input= Crystal Ball Output(50,000,000.00)At time t = 1High Price$18.16Low Price$12.17You make $43,000,000at t = 0 and there are nocash obligations nextperiod. The strategy ofinvesting in the projectand shorting calls resultsin sure profits of $43million today.PROBLEM 11-4GivenInitial investmentTotal Ore Quantity% Pure Copper/tonLife of projectOre mined each yearCost/ton for processingTax rateRisk free rateWACCGrowth in copper prices$$Solution Legend60,000,00075,000 tons15%5 years15,000 tons150.0030%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 OutputExpected PricesCopper Price/Tonper Ton$7,000 $7,0007,1507,8407,2008,7817,3009,8347,45011,015Forward Price Curve20112012201320142015Solutiona.RevenuesProcessingCostsDepreciation/DepletionNOINOPATPlus:DepreciationProject FCFRevenuesYear20112012201320142015ProcessingCostsDepreciation/DepletionNOINOPATPlus:DepreciationProject FCFBond PayoffsTotal payoffsb.NPVc.Year20112012201320142015NPVTracking portfolioYear20112012201320142015Cost at t = 0Total cost (Track. Port)Cost of investmentSavingsForward price$7,0007,1507,2007,3007,450Expected Price$7,0007,8408,7819,83411,015Gain (loss) on FORPROBLEM 11-5GivenRisk free rateSpot price (gold)Number of ouncesCost of 175 ouncesMaturityForward price (175 ounces)Solution Legend5.00%571.43175$ 100,000.001$ 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$SolutionStrategy of Client(Short gold today, invest in treasury and go long on forward contract)TODAYShort gold (175 ounces)Invest treasury (@ 5%)Long forward (@104,000)NetCash FlowNEXT YEAR$ 100,000.00 Cover short position$(100,000.00) Treasury bill payoff0 Close forward$NetCash Flow-PJim Lytle Strategy(Buy 175 ounces of gold today and sell next year)TODAYBuy gold (175 ounces)Borrow 100,000NetCash FlowNEXT YEAR$(100,000.00) Sell gold at P$ 100,000.00 Repay risk free loan$NetCash flowPP is the REALIZED price of 175ounce of gold next yearIf the price of 175 ounces of goldgoes above $106,000, Jim Lytle’sstrategy pays off more than theclient’s strategy. On the other hand ifthe price of 175 ounces of gold staysbelow $106,000, the client’s strategyprovides greater payoffs.PROBLEM 11-6GivenInitial investmentTotal PCs scrappedElectronic scrap per PCGold contentLife of projectPCs scrapped per yearTons of scrap per yearCurrent price of goldCost/ton for processingTax rateRisk free rateWACCGrowth in gold pricesForward Price Curve20112012201320142015$$$450,0001,000,00060.335200,000600592.8067.5030.0%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 Outputunitspoundsounce per tonyearsunitsper ounceGoldExpected PricesPrice/Ounceper Ounce$679.40 $634.30715.10678.70750.60726.21786.90777.04822.80831.43Solutiona.RevenuesProcessingCostsDepreciation/DepletionNOINOPATPlus:DepreciationProject FCFRevenuesYear20112012201320142015ProcessingCostsDepreciation/DepletionNOINOPATPlus:DepreciationProject FCFProcessingCostsDepreciation/DepletionNOINOPATPlus:Depreciationb.NPVc.Year20112012201320142015NPVTo solve for equivalent growth rate, use the following:Year20112012201320142015Expected PriceRevenuesNPVDifferenceUse Solver. Set difference to zero by changinggrowth rate cell (yellow highlighted)Project FCF

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