**Please submit all your work in the Excel file provided, called “Final Exam Data.”**

**Any evidence of cooperation among students on this exam will result in a zero score for the exam. Students may consult with instructor to ask clarifying questions while working on the exam. Students may use any additional resources, except consulting with each other.**

1. (5 points) Explain why the right to develop Probable (Possible) reserves is essentially an American call option on the net cash flows that follow from capital expenditures required for development. Put the answer in the worksheet labeled “Essay Answers.”

2. (10 points) What is the strike price of the call option, K, for Probable Reserves? Refer to Exhibit 5, which shows extraordinary capital expenditures in the first four years. Find the present value of these extraordinary capital expenditures. Assume discount rate equal to the risk-free rate 8.24%. Show your calculations in the worksheet labeled “Exhibit 5.”

3. (10 points) What is the strike price of the call option, K, for Possible Reserves? Refer to Exhibit 6, which shows extraordinary capital expenditures in the first six years. Find the present value of these extraordinary capital expenditures. Assume discount rate equal to the risk-free rate 8.24%. Show your calculations in the worksheet labeled “Exhibit 6.”

4. (15 points) Discuss the assumptions that have been made in the estimation of strike price. Put your answers in the worksheet labeled “Essay Answers.”

a. We implicitly assumed that Apache cannot decide not to make the second year’s expenditures once it has made the first year’s expenditures. What if that wasn’t true, how would that impact the ultimate value of the option?

b. We implicitly assumed that Apache will have to decide on the development of the entire MW Petroleum reserve at once, i.e. it cannot decide property by property. If that wasn’t true, how would that impact the ultimate value of the call option?

5. (10 points) What is the value of the underlying asset, S, for Probable Reserves? This is the value of the asset if Probable Reserves were already developed, i.e. if the extraordinary capital expenditures needed for development weren’t required. Calculate the present value of cash flows provided in Exhibit 5 but *excluding* the capital expenditures in years 1-4, and discounting at the rate of 13% (just like you did in MW Petroleum Assignment 2 for PUD). Show your calculations in the worksheet labeled “Exhibit 5.”

6. (10 points) Repeat the previous step for Possible Reserves using Exhibit 6 and excluding capital expenditures in years 1-6. Show your calculations in the worksheet labeled “Exhibit 6.”

7. (5 points) Is either of the call options (Probable Reserves, Possible Reserves) currently in the money? Show your work in Exhibit 5 and Exhibit 6, respectively.

8. (5 points) What is the time to expiration of the option, T? How long can Apache wait to develop the reserves? Find that information in the case. Put the answer in the worksheet labeled “Essay Answers.”

9. (30 points) Next, we should calculate the volatility of the underlying asset. Use the data for oil prices provided (worksheet “GARCH data”). Just like you did in your GARCH lab (steps 1 through 11), estimate the GARCH volatility of daily oil prices over the period 4/4/1983 through 12/31/1991 as this period roughly corresponds to the period depicted in Exhibit 8 of the case. For your initial guess, use Mu=0, Omega = 0.000002, Alpha = 0.07, and Beta = 0.92. When you use Solver, make sure you request “Answer” report. Plot the estimated daily volatility on a chart to show it is not constant over time. Calculate the average annualized GARCH volatility over the period. Average annualized volatility is calculated in three steps:

a. Average the daily GARCH volatility over the period of estimation.

b. Multiply the result of part a by 252 (the number of trading days in a year)

c. Take the square root of the result of part b. Round to two decimals.

Show all your work in the worksheet labeled “GARCH data.” Create a separate worksheet for the chart of daily volatility. Another worksheet called “Answer Report 1” will be generated automatically. Do not delete it. Points will be taken off if the Answer Report 1 worksheet is missing.

NOTE: If you decide to skip this step, then assume volatility 40%.

10. (30 points) Use T=6, volatility calculated in step 9 above, and risk-free rate of 8.24%. Use K and S from earlier questions, separately for Probable and for Possible Reserves. Assume no dividends. Value the real option on Probable Reserves and the real option on Possible Reserves. Show your calculations in Exhibit 5 and Exhibit 6, respectively.

11. (20 points) Now calculate the DCF value of Probable Reserves (using Exhibit 5) and the DCF value of Possible Reserves (using Exhibit 6) the same way you computed DCF of PUD (Exhibit 4) in MW Petroleum Lab 2. What can you say about the DCF value of these reserves compared to the real option valuation done in step 10 above? Show your calculations in Exhibit 5 and Exhibit 6, respectively.

12. (10 points) Comment on the following aspects of risk facing Apache’s potential lenders. Put your answers in the worksheet labeled “Essay Answers.”

a. Commodity price risk. Was it large, in your opinion, and what could Apache potentially do to alleviate this risk? Discuss the advantages and disadvantages of at least one hedging alternative.

b. Uncertainties regarding the volumes produced from MW Petroleum properties. Could those uncertainties be alleviated if Apache structured the financing transaction as Volumetric Production Payment (VPP)?

13. (10 points) If Apache arranged a project financing transaction, and borrowed 200 million with a 14% coupon rate for 10 years, they will have to pay a coupon every year, plus return the principal of $200 million at the end of the 10th year. Will they be able to pay the loan back with just the cash flows from Proved Developed Reserves? See Exhibit 3, item (19). Show your calculations in the worksheet labeled “Exhibit 3.”

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