Mayank

Emergency. My computer was down all day yesterday and Friday nite. Must have this questioned answered by 8pm tonite. So sorry.

Please fill out the answer worksheet tab 12-2 that's attached

12-2 CONCEPTUAL ANALYSIS OF REAL OPTIONS Huntsman Chemical is a relatively small chemical company located in Port Arthur, Texas. The firms management is contemplating its first international investment, which involves the construction of a petrochemical plant in So Paulo, Brazil. The proposed plant will have the capacity to produce 100,000 tons of the plastic pellets that are used to manufacture soft drink bottles. In addition, the plant can be converted over to produce the pellets used in the manufacture of opaque plastic containers such as milk containers. The initial plant will cost $50 million to build, but its capacity can later be doubled at a cost of $30 million, should the economics warrant it. The plant can be financed with a $40 million nonrecourse loan provided by a consortium of banks and guaranteed by the Export Import Bank. Huntsmans management is enthusiastic about the project, as its analysts think that the Brazilian economy is likely to grow into the foreseeable future. This growth, in turn, may offer Huntsman Chemical many additional opportunities in the future as the company becomes better known in the region. Based on a traditional discounted cash flow analysis, Huntsmans analysts estimate that the project has a modest NPV of about $5 million. However, when Huntsmans executive committee members review the proposal, they express concern about the risk of the venture, based primarily on their view that the Brazilian economy is very uncertain.Toward the close of their deliberations, the company CEO turns to the senior financial analyst and asks him whether he has considered something the CEO has recently read about called real options in performing his discounted cash flow estimate of the projects NPV.

Assume the role of the senior analyst and provide your boss with a brief discussion of the various options that may be embedded in this project, and very roughly sketch out how these options can add to the value of the project. (Hint: No computations are required.) Titman, Sheridan; Martin, John D. (2014-04-08). Valuation (2nd Edition) (Prentice Hall Series in Finance) (Page 475). Prentice Hall. Kindle Edition.

PROBLEM 12-1 Given Quantity Price (Year 0) P-high P-low Forward price Extraction costs Solution Legend $ $ $ $ $ 1000 20 25 15 20 17 = 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 You can lock into the forward rate or sell immediately at the same spot rate. The payoffs under either action is the same. Selling today is better because of time value of money. Profit (sell today) Cert. Equiv (sell forward) Uncertain Profits Profit-high Extract oil only in this state of the world Profit-low Do not extract oil in this state of the world Risk neutral probability Value of public land a. b. Equate forward price = expected cash flows based on risk neutral probabilities: 20 = 25 * p + 15 * (1 - p). PROBLEM 12-2 a. b. c. d. e. 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 PROBLEM 12-3 Given Solution Legend VARIATION IN PROBLEM: High price of copper is 2.8 and low price is 1.2 = Value given in problem Ore purity Ore quantity (lbs) Current price P-high P-low Expected price Forward price Development costs Amount payable today Amount due next year Extraction costs (per lb of copper) = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output $ $ $ $ $ $ $ 0.375 5,000,000 2.20 2.80 1.20 2.50 2.31 1,200,000.00 75.00% 25.00% 1.60 Cost of capital (exploration) Cost of capital (development) Risk free rate 25.00% 15.00% 5.00% Solution a. Value of the hedged lease Certainty Equivalent cash flows NPV Risk neutral probability Risk neutral probability b. Value of the undhedged lease without any option In the high price scenario In the low price state Certainty equivalent NPV Note: Extraction costs of $1.60 incurred at the beginning of the second year is shifted to the end of the second year by multiplying by the risk free rate. This makes all cash flows in the computation consistent (with regard to timing of cash flows). NPV of project if Newport commits to production today and locks in a forward price. Use forward price to calculate the risk neutral probability, i.e., Use todays' price to calculate the risk neutral probability, i.e., c, d. Value of the (unhedged) lease with option In the high price scenario In the low price state Certainty equivalent NPV Current Risk Free Low 1 Rate Price Risk Neutral Price Low Probability High Price Price Value of the (unhedged) lease without any real option Value of the (unhedged) lease with real option e. Strategy of short positions on 1.875m lbs. call options (exercise price = $1.68, maturity = 2, call premium = $0.70/lb) and long position in project. Price = $2.80 Price = $1.20 Gain/loss on options Gain/loss on production Net payoffs at t = 2 Payoff from sale of option (at t = 1) Investment in project Net cash flows at t = 0 This strategy resullts in a sure profit of Fair price of option PROBLEM 12-4: Valuation an American Option Given Risk-neutral probability Risk free Interest rate Discount factor = exp(Risk free interest rate) Strike (in $ millions) 0.4626 5% $ 23.00 Solution Today Year One Year Two Year Three $ $ Text Color Legend Value of Beginning Oil Field Operations Now $ NPV of waiting (NPV-Waiting) NPV of Exercising Now (NPV-Now) Value of American Option = max (NPV-Waiting,NPV-Now) $ $ 14.5700 31.7800 28.1900 25.000 19.6600 $ $ 26.5500 $ $ 35.8300 23.5500 20.8800 Cell Outline Legend $ 17.4400 Stock Wait Exercise a. b. 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 PROBLEM 12-5 Given Price of Gas Solution Legend $ 8.00 Price of Fuel Oil Max Most likely Minimum Revenues WACC $ 12.00 $ 2.00 $ 10.00 10% = 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 a. Estimate the power plant's cash flow Revenues Less: Fuel cost Jet fuel cost (uncertain) Cash flow b. c. $ 10.00 $ 7.00 PROBLEM 12-6 STATIC ANALYSIS (based on expected prices of gas and Jet fuel) Margin analysis per barrel of crude processed Gasoline Jet Fuel Price/bbl of output $ $ Qty of output/bbl of crude 0.9 0.7 Revenue/bbl of crude $ $ Cost/bbl of crude $ 25.00 $ 25.00 Proc cost/bbl of crude $ $ Gross Profit/bbl of crude $ (25.00) $ (25.00) Given Cost of building the refinery $ 2,000,000,000 Refinery life 5 years Depreciation = straight line with no salvage value Gasoline prices (next year) Maximum $ Most likely $ Minimum $ Expected price $ Jet fuel prices (next year) $ $ $ $ Refining capacity Crude oil in bbls Conversion to gasoline Conversion to jet fuel Cost of purchasing crude/bbl $ Other costs of refining Cost of capital Tax rate Riskfree rate 4.00 2.50 1.75 - Maximum Most likely Minimum Expected price 5.00 3.25 2.50 12,000,000 90% 70% 25.00 35% price of fuel 10% 30% 5.5% 1 Price of gasoline Price of jet fuel Revenues Gasoline Jet fuel Revenues for Output Choice Less: Cost of purchasing crude Less: Cost of refining Less: Depreciation EBIT Less: Taxes NOPAT Plus: Depreciation Cash flow a. NPV Switch to jet fuel b. This implies that jet fuel is preferable (provides higher margins) Revenures (Jet Fuel) $ Cost of purchasing crude $ (300,000,000) Cost of refining $ Depreciation $ (400,000,000) EBIT $ (700,000,000) Less: Taxes $ 210,000,000 NOPAT $ (490,000,000) Depreciation $ 400,000,000 Project FCF $ (90,000,000) NPV $ (2,341,170,809) 2 Year 3 4 5 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 Negative NPV based on expected prices of jet fuel PROBLEM 12-7 Do nothing Property 1 Units Rent/month $ Yearly revenues Potential value Solution Legend 4 2,000 = 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 Property 2 Units Rent/month Yearly revenues Potential value 4 $ 1,500 New construction Units 10 Rent/month $ 2,500 Yearly revenues Value Cost $ 1,500,000 NPV Assume: risk free rate of 5% and volatility of 20% r 0.05 T 1 sigma 0.2 X 1500000 Underlying 3000000 d1 N(d1) d2 N(d2) Basic Call value to calculate NPV Property 1 NPV Property 2 call a. b. c. Property 2 has a greater NPV because forgeone value is less. PROBLEM 12-8 Given Risk free rate Dividend yield Exercise price (I) Current value (V) Volatility Volatility ^2 NPV $ $ $ 5% 10% 50,000,000 45,000,000 20% 0.0400 (5,000,000) The right to develop the casino can be thought of as a American Call Option with infinite life. Immediate exercise of this option results in a negative NPV (-50 m + 45 m = -5 million). However, the real estate development option has a value of $3.317 million because of the inherent uncertainty in the prospects of the casino industry in that region. This uncertainty suggest that it may be worth waiting. Solution Call Option Value V* Call (Infinite life option) NPV* Casino Development Option Value Critical Value Critical NPV value 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 PROBLEM 12-1 Given Quantity Price (Year 0) P-high P-low Forward price Extraction costs Solution Legend $ $ $ $ $ 1000 20 25 15 20 17 = 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 You can lock into the forward rate or sell immediately at the same spot rate. The payoffs under either action is the same. Selling today is better because of time value of money. Profit (sell today) Cert. Equiv (sell forward) Uncertain Profits Profit-high Extract oil only in this state of the world Profit-low Do not extract oil in this state of the world Risk neutral probability Value of public land a. b. Equate forward price = expected cash flows based on risk neutral probabilities: 20 = 25 * p + 15 * (1 - p). PROBLEM 12-2 a. b. c. d. e. 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 PROBLEM 12-3 Given Solution Legend VARIATION IN PROBLEM: High price of copper is 2.8 and low price is 1.2 = Value given in problem Ore purity Ore quantity (lbs) Current price P-high P-low Expected price Forward price Development costs Amount payable today Amount due next year Extraction costs (per lb of copper) = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output $ $ $ $ $ $ $ 0.375 5,000,000 2.20 2.80 1.20 2.50 2.31 1,200,000.00 75.00% 25.00% 1.60 Cost of capital (exploration) Cost of capital (development) Risk free rate 25.00% 15.00% 5.00% Solution a. Value of the hedged lease Certainty Equivalent cash flows NPV Risk neutral probability Risk neutral probability b. Value of the undhedged lease without any option In the high price scenario In the low price state Certainty equivalent NPV Note: Extraction costs of $1.60 incurred at the beginning of the second year is shifted to the end of the second year by multiplying by the risk free rate. This makes all cash flows in the computation consistent (with regard to timing of cash flows). NPV of project if Newport commits to production today and locks in a forward price. Use forward price to calculate the risk neutral probability, i.e., Use todays' price to calculate the risk neutral probability, i.e., c, d. Value of the (unhedged) lease with option In the high price scenario In the low price state Certainty equivalent NPV Current Risk Free Low 1 Rate Price Risk Neutral Price Low Probability High Price Price Value of the (unhedged) lease without any real option Value of the (unhedged) lease with real option e. Strategy of short positions on 1.875m lbs. call options (exercise price = $1.68, maturity = 2, call premium = $0.70/lb) and long position in project. Price = $2.80 Price = $1.20 Gain/loss on options Gain/loss on production Net payoffs at t = 2 Payoff from sale of option (at t = 1) Investment in project Net cash flows at t = 0 This strategy resullts in a sure profit of Fair price of option PROBLEM 12-4: Valuation an American Option Given Risk-neutral probability Risk free Interest rate Discount factor = exp(Risk free interest rate) Strike (in $ millions) 0.4626 5% $ 23.00 Solution Today Year One Year Two Year Three $ $ Text Color Legend Value of Beginning Oil Field Operations Now $ NPV of waiting (NPV-Waiting) NPV of Exercising Now (NPV-Now) Value of American Option = max (NPV-Waiting,NPV-Now) $ $ 14.5700 31.7800 28.1900 25.000 19.6600 $ $ 26.5500 $ $ 35.8300 23.5500 20.8800 Cell Outline Legend $ 17.4400 Stock Wait Exercise a. b. 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 PROBLEM 12-5 Given Price of Gas Solution Legend $ 8.00 Price of Fuel Oil Max Most likely Minimum Revenues WACC $ 12.00 $ 2.00 $ 10.00 10% = 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 a. Estimate the power plant's cash flow Revenues Less: Fuel cost Jet fuel cost (uncertain) Cash flow b. c. $ 10.00 $ 7.00 PROBLEM 12-6 STATIC ANALYSIS (based on expected prices of gas and Jet fuel) Margin analysis per barrel of crude processed Gasoline Jet Fuel Price/bbl of output $ $ Qty of output/bbl of crude 0.9 0.7 Revenue/bbl of crude $ $ Cost/bbl of crude $ 25.00 $ 25.00 Proc cost/bbl of crude $ $ Gross Profit/bbl of crude $ (25.00) $ (25.00) Given Cost of building the refinery $ 2,000,000,000 Refinery life 5 years Depreciation = straight line with no salvage value Gasoline prices (next year) Maximum $ Most likely $ Minimum $ Expected price $ Jet fuel prices (next year) $ $ $ $ Refining capacity Crude oil in bbls Conversion to gasoline Conversion to jet fuel Cost of purchasing crude/bbl $ Other costs of refining Cost of capital Tax rate Riskfree rate 4.00 2.50 1.75 - Maximum Most likely Minimum Expected price 5.00 3.25 2.50 12,000,000 90% 70% 25.00 35% price of fuel 10% 30% 5.5% 1 Price of gasoline Price of jet fuel Revenues Gasoline Jet fuel Revenues for Output Choice Less: Cost of purchasing crude Less: Cost of refining Less: Depreciation EBIT Less: Taxes NOPAT Plus: Depreciation Cash flow a. NPV Switch to jet fuel b. This implies that jet fuel is preferable (provides higher margins) Revenures (Jet Fuel) $ Cost of purchasing crude $ (300,000,000) Cost of refining $ Depreciation $ (400,000,000) EBIT $ (700,000,000) Less: Taxes $ 210,000,000 NOPAT $ (490,000,000) Depreciation $ 400,000,000 Project FCF $ (90,000,000) NPV $ (2,341,170,809) 2 Year 3 4 5 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 Negative NPV based on expected prices of jet fuel PROBLEM 12-7 Do nothing Property 1 Units Rent/month $ Yearly revenues Potential value Solution Legend 4 2,000 = 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 Property 2 Units Rent/month Yearly revenues Potential value 4 $ 1,500 New construction Units 10 Rent/month $ 2,500 Yearly revenues Value Cost $ 1,500,000 NPV Assume: risk free rate of 5% and volatility of 20% r 0.05 T 1 sigma 0.2 X 1500000 Underlying 3000000 d1 N(d1) d2 N(d2) Basic Call value to calculate NPV Property 1 NPV Property 2 call a. b. c. Property 2 has a greater NPV because forgeone value is less. PROBLEM 12-8 Given Risk free rate Dividend yield Exercise price (I) Current value (V) Volatility Volatility ^2 NPV $ $ $ 5% 10% 50,000,000 45,000,000 20% 0.0400 (5,000,000) The right to develop the casino can be thought of as a American Call Option with infinite life. Immediate exercise of this option results in a negative NPV (-50 m + 45 m = -5 million). However, the real estate development option has a value of $3.317 million because of the inherent uncertainty in the prospects of the casino industry in that region. This uncertainty suggest that it may be worth waiting. Solution Call Option Value V* Call (Infinite life option) NPV* Casino Development Option Value Critical Value Critical NPV value 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 PROBLEM 12-1 Given Quantity Price (Year 0) P-high P-low Forward price Extraction costs Solution Legend $ $ $ $ $ 1000 20 25 15 20 17 = 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 You can lock into the forward rate or sell immediately at the same spot rate. The payoffs under either action is the same. Selling today is better because of time value of money. Profit (sell today) Cert. Equiv (sell forward) Uncertain Profits Profit-high Extract oil only in this state of the world Profit-low Do not extract oil in this state of the world Risk neutral probability Value of public land a. b. Equate forward price = expected cash flows based on risk neutral probabilities: 20 = 25 * p + 15 * (1 - p). PROBLEM 12-2 a. b. c. d. e. 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 PROBLEM 12-3 Given Solution Legend VARIATION IN PROBLEM: High price of copper is 2.8 and low price is 1.2 = Value given in problem Ore purity Ore quantity (lbs) Current price P-high P-low Expected price Forward price Development costs Amount payable today Amount due next year Extraction costs (per lb of copper) = Formula/Calculation/Analysis required = Qualitative analysis or Short answer required = Goal Seek or Solver cell = Crystal Ball Input = Crystal Ball Output $ $ $ $ $ $ $ 0.375 5,000,000 2.20 2.80 1.20 2.50 2.31 1,200,000.00 75.00% 25.00% 1.60 Cost of capital (exploration) Cost of capital (development) Risk free rate 25.00% 15.00% 5.00% Solution a. Value of the hedged lease Certainty Equivalent cash flows NPV Risk neutral probability Risk neutral probability b. Value of the undhedged lease without any option In the high price scenario In the low price state Certainty equivalent NPV Note: Extraction costs of $1.60 incurred at the beginning of the second year is shifted to the end of the second year by multiplying by the risk free rate. This makes all cash flows in the computation consistent (with regard to timing of cash flows). NPV of project if Newport commits to production today and locks in a forward price. Use forward price to calculate the risk neutral probability, i.e., Use todays' price to calculate the risk neutral probability, i.e., c, d. Value of the (unhedged) lease with option In the high price scenario In the low price state Certainty equivalent NPV Current Risk Free Low 1 Rate Price Risk Neutral Price Low Probability High Price Price Value of the (unhedged) lease without any real option Value of the (unhedged) lease with real option e. Strategy of short positions on 1.875m lbs. call options (exercise price = $1.68, maturity = 2, call premium = $0.70/lb) and long position in project. Price = $2.80 Price = $1.20 Gain/loss on options Gain/loss on production Net payoffs at t = 2 Payoff from sale of option (at t = 1) Investment in project Net cash flows at t = 0 This strategy resullts in a sure profit of Fair price of option PROBLEM 12-4: Valuation an American Option Given Risk-neutral probability Risk free Interest rate Discount factor = exp(Risk free interest rate) Strike (in $ millions) 0.4626 5% $ 23.00 Solution Today Year One Year Two Year Three $ $ Text Color Legend Value of Beginning Oil Field Operations Now $ NPV of waiting (NPV-Waiting) NPV of Exercising Now (NPV-Now) Value of American Option = max (NPV-Waiting,NPV-Now) $ $ 14.5700 31.7800 28.1900 25.000 19.6600 $ $ 26.5500 $ $ 35.8300 23.5500 20.8800 Cell Outline Legend $ 17.4400 Stock Wait Exercise a. b. 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 PROBLEM 12-5 Given Price of Gas Solution Legend $ 8.00 Price of Fuel Oil Max Most likely Minimum Revenues WACC $ 12.00 $ 2.00 $ 10.00 10% = 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 a. Estimate the power plant's cash flow Revenues Less: Fuel cost Jet fuel cost (uncertain) Cash flow b. c. $ 10.00 $ 7.00 PROBLEM 12-6 STATIC ANALYSIS (based on expected prices of gas and Jet fuel) Margin analysis per barrel of crude processed Gasoline Jet Fuel Price/bbl of output $ $ Qty of output/bbl of crude 0.9 0.7 Revenue/bbl of crude $ $ Cost/bbl of crude $ 25.00 $ 25.00 Proc cost/bbl of crude $ $ Gross Profit/bbl of crude $ (25.00) $ (25.00) Given Cost of building the refinery $ 2,000,000,000 Refinery life 5 years Depreciation = straight line with no salvage value Gasoline prices (next year) Maximum $ Most likely $ Minimum $ Expected price $ Jet fuel prices (next year) $ $ $ $ Refining capacity Crude oil in bbls Conversion to gasoline Conversion to jet fuel Cost of purchasing crude/bbl $ Other costs of refining Cost of capital Tax rate Riskfree rate 4.00 2.50 1.75 - Maximum Most likely Minimum Expected price 5.00 3.25 2.50 12,000,000 90% 70% 25.00 35% price of fuel 10% 30% 5.5% 1 Price of gasoline Price of jet fuel Revenues Gasoline Jet fuel Revenues for Output Choice Less: Cost of purchasing crude Less: Cost of refining Less: Depreciation EBIT Less: Taxes NOPAT Plus: Depreciation Cash flow a. NPV Switch to jet fuel b. This implies that jet fuel is preferable (provides higher margins) Revenures (Jet Fuel) $ Cost of purchasing crude $ (300,000,000) Cost of refining $ Depreciation $ (400,000,000) EBIT $ (700,000,000) Less: Taxes $ 210,000,000 NOPAT $ (490,000,000) Depreciation $ 400,000,000 Project FCF $ (90,000,000) NPV $ (2,341,170,809) 2 Year 3 4 5 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 Negative NPV based on expected prices of jet fuel PROBLEM 12-7 Do nothing Property 1 Units Rent/month $ Yearly revenues Potential value Solution Legend 4 2,000 = 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 Property 2 Units Rent/month Yearly revenues Potential value 4 $ 1,500 New construction Units 10 Rent/month $ 2,500 Yearly revenues Value Cost $ 1,500,000 NPV Assume: risk free rate of 5% and volatility of 20% r 0.05 T 1 sigma 0.2 X 1500000 Underlying 3000000 d1 N(d1) d2 N(d2) Basic Call value to calculate NPV Property 1 NPV Property 2 call a. b. c. Property 2 has a greater NPV because forgeone value is less. PROBLEM 12-8 Given Risk free rate Dividend yield Exercise price (I) Current value (V) Volatility Volatility ^2 NPV $ $ $ 5% 10% 50,000,000 45,000,000 20% 0.0400 (5,000,000) The right to develop the casino can be thought of as a American Call Option with infinite life. Immediate exercise of this option results in a negative NPV (-50 m + 45 m = -5 million). However, the real estate development option has a value of $3.317 million because of the inherent uncertainty in the prospects of the casino industry in that region. This uncertainty suggest that it may be worth waiting. Solution Call Option Value V* Call (Infinite life option) NPV* Casino Development Option Value Critical Value Critical NPV value 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