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INTRUCTIONS – Please use pocket calculator and show workings neatly under each question.
1. If 8.5% is the nominal rate of interest quoted by the bank and the real rate of interest is 2.5% what is the expected rate of inflation?
2. A bulldozer cost $1.3M in December 2013. What would its price be in December 2014 and April 2015 if over the intervening period it escalated in real terms at a rate of 1.0% per annum and general inflation averaged 2.5% per annum?
3. If the price of a mineral commodity was $3500/t in 1st June 2014 and $4000/t on 30 September 2015 what was the average annual rate of nominal price escalation? Please calculate it based on trading days and continuously.
4. The real dollar estimate of the capital cost of a mining project is $100M to be be invested over a 2-years pre-production period with $30 spent in year 1 and the reminder in year 2. We estimate that 10% of the expenditure in each year is in exploration and feasibility 30% in normal depreciable assets and the reminder in pooled project assets. Please work out the annual rate of depreciation in year 3, assuming that assets start depreciating then, if the production life of the project is 4 years and the weighted average useful life of normal assets is 8 years
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5. What is the probability of Gambler’s ruin if one can fund 6 exploration projects with a 5% chance of success in each project? Assume that the value of one exploration success is sufficient to guarantee survival.
6. A project has a 15% chance of a net $500M value and a cost of $25M. What are its EV and its Certainty equivalent if our RT is $60M?
7. A reference exploration area contains the following projects valued at $M 7.6, 16.1, 19.6, 29.7, 107.4, 64.2, 416.0, 157.8, 34.2, 84.8, 175.9, 890, 988.9. Please calculate the mean and standard deviation of the values keeping in mind that they are lognormally distributed.
8. Compute the percentiles and cumulative distribution of the above data set using both the inclusive and exclusive methods and from each of them derive the mean using the Swanson method.
9. The prior probability of discovery by drilling randomly a broadly geologically/geochemically defined target area is 5%. We are offered a geophysical survey which will refine our targeting by providing anomalies 85% (true positives) of the time it is run on mineralised sites but also 7% of the time when run on barren survey stations (false positives). What is the posterior probability of discovery given that we drill an anomaly?
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