1. In what way is the development of a copper mine like Antamina a real option? In what way is the bidding structure put in place by the Peruvian government an option?
The mine had a valuable real option component, in the form of the right to develop the mine after completing exploration. The Peruvian government requested the bidders to state both the premium that they would pay and exercise price (development expenditure) they would set for this real option.
What is the correspondence between these real options and financial options? Theoretically real options and financial options are very similar, however real options are usually solved through numerical methods (ex post) the binomial method or Monte Carlo simulation, since these methods allows more flexibility for setting up scenarios.
What other real options does the owner of Antamina have? There are basically three options: •Option to Abandon •Option to Abandon at year 2 with penalty •Option of Early Development
2. Conceptually, how would you build a real options model to value the Antamina project? What data and assumptions would you need?
Sources of Uncertainty (Variables)
Revenues: Mine’s Life (approach = deterministic) Future Prices of zinc and copper (approach = stochastic on years 0 to 2) Quantity of Ore (Monte Carlo) Costs: Operations Expenses (Monte Carlo) Capital Expenditures (Monte Carlo)
The spreadsheet, bid.xls, implements one model of the real options in Antamina. You should try to “figure out” how it works through reverse engineering.
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According to the workbook intructions. (1) “Summary” — This worksheet takes as inputs the initial payment, the investment commitment, and the number of trials that the simulation is supposed to run for. Outputs: the amount of the bid, the NPVof the mine without the option to abandon (Section A) , the NPV of the mine with the option to abandon after 2 years, without penalty (Section B), the NPV of the mine with the option to abandon after paying the penalty described Section C).
This worksheet also shows the penalty to be paid as a function of the investment commitment and the required investment for each of the three scenarios.
(2) “Parameters” – This worksheet has all the input parameters required to calculate the WACC, inflation rates, and other capital markets data used by the DCF calculations. It also allows the user to change the probability of each of the three outcomes for the mine ore quantity. The lower portion of the worksheet has all the parameters required to calculate the paths for the copper and zinc prices and convenience yields. The drift rates are the long-run trend of copper prices, which are assumed random around the long-run trend. The convenience yields are modeled as mean reverting processes, which tend to oscillate around their means. A measure of how quickly this oscillation happens is given by the mean reversion parameter. The correlations between the commodity prices and convenience yields are also included.
(3) “Simulation Summary” – This worksheet has the summary statistics from each of the runs, which areshown in (4) “Simulation Results”.
(5) “2-yr prices” – This worksheet has the monthly copper and zinc prices and convenience yields as calculated by the Monte Carlo model. For each run, a price and convenience yield path is constructed on a monthly basis according to the commodity’s volatility, mean reversion parameters, and correlations with the other parameters. The final price and convenience yield path (at month 24, 2 years), is used as input to calculate a 20 year forward curve of copper and zinc prices, which is then input into the DCF analysis to model the future prices of copper and zinc.
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(6)-(8) DCF spreadsheets – These three spreadsheets have a full DCF analysis of the mine for the three quantity scenarios described in the case.
(9) “Macro” – This worksheet is the macro that drives the Monte Carlo simulation.
General Model: Basically what the model does is to calculate the PV of cash flows of the three different probability scenarios (high, expected, low) and the register the value obtained in the simulations results sheet, the three different values obtained are the weighted averaged according to the probabilities defined in the parameters sheet. This process iterates according to the number of trials set in the summary sheet.
Option 1: In case that the PV is negative then the model automatically identifies this event, the real option is exercised and the PV is recorded then as 0 in another column for this particular simulation trial. The value of the investment is then weighted summed for values of PV > 0.
Option 2: The process is identical as the one described above, only that in case that the value of the investment is lower than the one initially committed then a penalty is applied. The penalty is calculated as followed: committed investment less real investment times 30%
After the number of trials is completed then the model proceeds to calculate the value of the project according to the following scenarios:
•No option to abandon: Mean of weighted averaged PVs, less the required investment (High scenario) less the feasibility study equals the project NPV
•Option to abandon at year 2: Mean of weighted averaged PVs, less the required investment (Average) less the feasibility study equals the project NPV
•Option to abandon at year 2 with penalty: Mean of weighted averaged PVs, less the required investment (average) less the penalty less the feasibility study less initial payment equals the project NPV
What are the key assumptions and limitations of the model? How could it be improved?
Apart from the obvious sources of uncertainty, the model works with a set of defined outcome probabilities for the high, expected and low scenarios. These are based on “expert” opinion, meaning that the results could be biased.
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With the available information from the previous email regarding the projects of Juniper, Palomino and Stargazer, I feel it is in the company’s best interest to go with the Palomino project moving forward. The reason for not selecting the other two options is because Juniper carries too low of a risk for completion. Stargazer is not worth the high risk of completion and the unfamiliarity of how ...
The model assumes no uncertainty from prices after year two, which is not totally accurate; companies do no usually hedge to 100%, especially when volumes are so high.
3. Using the spreadsheet, bid.xls, calculate values for the project, and then submit a bid representing how much you will pay for the property. You may work in teams, but identify the members of your team when submitting your bid. You will submit three different bids, each one under a different set of auction procedures:
•If the winning bidder was legally forced to develop Antamina after completing the exploration phase, and was required to pay the Peruvian government up- front for this project, what is the most they would be willing to pay?
The should pay only the initial investment of $17.50
•If the winning bidder could choose to whether or not to develop Antamina at the end of two years, but was required to pay the Peruvian government a single fee up-front for the right to develop the project, what is the most they would be willing to pay? Under this alternative, there is no investment commitment or penalty; the firm merely pays the government up front, and has the right to develop at the end of two years. If they don’t develop at year two, they lose the right to develop the field.
The difference between the value of the project with option to aband and the value of the project with no option, for example:
PV (Option) $1,662.31 – Pv (No option) $1,366.52 = $ 295.79 Value of the option
•Under the current bidding rules, the winning bidder states both an initial cash payment as well as an investment commitment that is paid only if they choose to develop the field. Bids are evaluated by summing up-front amount and 30% of the investment commitment. If you proceed with development, but fail to spend the full investment commitment, the Peruvian government will fine you 30% of the difference. What is the most that you would be willing to bid under these rules? How would you trade off these two components of the bid?
PV (Option with Penalty) $1,664.15 – Pv (No option) $1,366.52 = $ 277.63 Value of the option with penalty
4. What are the incentives brought about by the different auction rules?Do the rules seem to meet what you perceive to be the goals of the Peruvian government? What the government seeks is not only to secure the development of the mine but also the committed capital from firms participating in the auction.
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