PROBLEM 12-5: Valuation an American Option Given Risk-neutral probability Risk f

Question

PROBLEM 12-5: 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 Toda Year One Year Two Year Three $ 35.8300 $ 31.7800 $ 28.1900 $ 26.5500 Text Color Legend Value of Beginning Oil Field Operations Now $25.000 $ 23.5500 NPV of waiting (NPV-Waiting) NPV of Exercising Now (NPV-Now) Value of American Option = max (NPV-waiting,NPV-Now) $ 20.8800 $19.6600 Cell Outline Legend Stock Wait $17.4400 14.5700 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

Explanation / Answer

Answer Year Lease Property Development of property Cash Inflow(WN 1) Present Value factor PV of Cashflow 0 -25 -23 -48 1 -48 1 24.26 0.95 23.11 2 23.55 0.91 21.36 3 22.85 0.86 19.74 Net Present Value 16.20 As the NPV of the project is positive, J & B should drill from the very next day i.e. From today itself. Working Note 1 Cashinflow for year 1 on joint probability basis Probability for uplift %(a) Cash inflow in such condition(b) a*b Yes 46% 28.19 13.04 No 54% 20.88 11.22 Year 1 Cash Inflow 24.26 Cashinflow for year 2 on joint probability basis Probability for uplift(Yr 1) %(a) Probability for uplift %(b) Joint Probability(a*b) Cash inflow in such condition Cashflow*Joint Probability Yes 46% Yes 46% 21% 31.78 6.80 46% No 54% 25% 23.55 5.85 No 54% Yes 46% 25% 23.55 5.85 54% No 54% 29% 17.44 5.04 Year 2 Cash Inflow 23.55 Cashinflow for year 3 on joint probability basis Probability for uplift(Yr 1) %(a) Probability for uplift(Year 2) %(b) Probability for uplift(Year 3) %(c) Joint Probability(a*b*c) Cash inflow in such condition Cashflow*Joint Probability Yes 46% Yes 46% Yes 46% 10% 35.83 3.55 Yes 46% Yes 46% No 54% 12% 26.55 3.05 Yes 46% No 54% Yes 46% 12% 26.55 3.05 Yes 46% No 54% No 54% 13% 19.66 2.63 No 54% Yes 46% Yes 46% 12% 26.55 3.05 No 54% Yes 46% No 54% 13% 19.66 2.63 No 54% No 54% Yes 46% 13% 19.66 2.63 No 54% No 54% No 54% 16% 14.57 2.26 Year 3 Cash Inflow 22.85

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