Representations are given of the value of optioning a buy-in position to an exploration project based on both the Cozzolino risk adjusted value (RAV) formula as well as on the parabolic RAV formula; numerical illustrations indicate that there is little difference between maximal option values based on either formula. For deterministic values of success probability, ps, gain, G, costs. C, corporate risk tolerance, RT, and working interest, W, illustrations are given of the maximum option value in relation to the RAV. In addition, when probability distributions for Ps, G, C, RT and W are taken to represent ±10% or ±20% variations around fixed mean parameter values, it is shown that the corresponding cumulative probability distributions for maximum option value are remarkably similar when based on either the Cozzolino or parabolic RAV formula. It is also shown that contributions of equal fractional variations of ps, G, C, RT and W to the variance in the maximum option value are extremely unequal in relative importance and, further, increasing the variations from ± 10% to ± 20% not only causes a four-fold increase of the volatility around the mean option value, but also causes a 20% decrease in the mean, as well as re-ordering the relative importance of factors contributing to the variance around the mean option value. For massive variations of ps, G, C, or RT, which occur outside of initial estimated ranges, it is shown that the maximum option value (or the desired working interest) has to be adjusted either to keep total project costs at a fixed level or, if the working interest is fixed, then while the total project costs increase, the RAV decreases faster than the maximum potential value, so that the maximum option value increases. The purpose of these computations has been to illustrate explicitly how one can quantify uncertainty in option decisions at the start of an exploration project, when information is normally inaccurate and imprecise, and also how one can use later unanticipated changes in success probability, costs, gains, or corporate risk tolerance to immediately re-evaluate both the RA V of the project, the maximum worth of the option, and a new working interest to minimize or hold constant total project costs including the option cost.
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