Oil Field Valuation – An Real Option Based Analysis
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An Illustrative Example The valuation of a hypothetical oilfield has been done on the basis of a mathematical model based on the theory presented in the previous section. The aim is to elucidate the implementation of the model through means of this example. Moreover, an understanding of the impact of variation of key parameters on the valuation results is sought to be achieved through the model. Parameter Values and Assumptions The values of the different parameters used in the example are given in the table below
Table 4.1 – Parameter values used in base case analysis Simplifying assumptions in assigning Parameter Value Annual production costs have been assumed to be a function of the amount of oil produced in a year. Similarly capital costs and depreciation costs have been assigned a fixed value per barrel of oil produced. This is based on the assumption that the amount of oil that needs to be produced is the key driver of capital expenditure and consequently of depreciation An annual production rate has been assumed over a 7 year period rather than using a specified production schedule. This has been done to make the model more generic. Further generality can be added by designing the model to accommodate any given production schedule. Other values have been taken the same as that in the example used in the paper detailing the model. Stage wise Results Stage III As described in the previous section the calculation starts from the point when there is no oil left in the field and the field value is zero. Using the difference equation which gives the dynamics of variation of field value with spot prices and quantity of oil left, the value of the field is calculated for increasing amounts of unexploited oil reserves. Fig 4.1 presents the variation of field value with amount of oil left in the field. 
Fig 4.1
It can be observed that rise in field value is more or less a linear function of the amount of oil unextracted when the spot price is close to the long term average spot price. For spot prices higher than the long term average spot price, the rate of increase in field value decreases with quantity of oil unextracted. This is as expected due to the mean reverting characteristic of oil prices. Similarly, for oil prices lower than the Ŝ, the rate of increase in field value is also on the rise as there is more chance of oil price reaching close to Ŝ, the more there is time left for extraction (a function of amount of unextracted oil). Next the variation of oil field value with spot price at different levels of extraction is observed. As expected, lesser the amount of oil left in the field (and consequently, lesser the extraction period) the more linear is the relationship of field value with spot prices. When a large part of the reserves is unextracted, the incremental benefit of an increase in spot price is less pronounced as the mean reverting nature of the oil prices reduces the expected value of cash flows over the life of the field. 
Fig 4.2
Stage II In this stage, the value of the field when the development of the field is ongoing is developed. Fig 4.3 presents the variation of field value over this period for different values of spot prices. Again it can be seen that the higher the spot price above Ŝ, the faster is the decline in value of the field and at the same time for spot prices below Ŝ, the field value increases as the spot value is expected to rise with time. 
Fig 4.3
In Fig 4.4, the relationship between field value and spot prices is plotted for different points of development in Stage II. Again the mean reverting behaviour of oil prices is displayed as the value of a fully developed field exceeds that of the one on which development is yet to commence for high values of spot prices. The relationship is exactly the opposite for low oil prices as the greater the time to extraction, the more the likelihood that that the price will rise by the time extraction begins. 
Fig 4.4
This stage takes the value of the field at the beginning of the development period and considers whether it is worthwhile to develop the field by weighing it against the present value of the development costs. The variation of the value of the oil field with the amount of time left to exercise the development option is given Fig 4.5. It can be seen, that below a critical spot price, the value of the field increases as the amount of time to expiry increases, till it reaches a plateau. This is unlike the case of stock options where option value increases with increase in time to maturity. The flat nature of the curve beyond a particular nature of time to expiry is a result of the mean reverting nature of oil prices limiting the upside that can be obtained through the deal. Moreover, it is also observed that for high levels of spot prices, the optimal decision is to exercise the development option immediately. This is also intuitive as one would like to gain maximum benefit of the high spot prices before mean reversion pulls it down. 
Fig 4.5 – Variation of Oil Field Value with time left for exercise of Development Option Trends in Valuation An analysis of change in valuation results with change in the values of key parameters was carried out to develop a better understanding of the nature of relationships between them. Development costs This is a key parameter in the valuation of oil fields by the real options method. In many ways it is equivalent to the concept of the strike price used in the case of stock options. A lesser value of development costs can cause a change in decision from abandonment of the oil field to its development and vice versa. Table 4.2 presents the variation of critical spot price with change in development costs. The critical spot price is the value of spot the end of the development option, below which it is optimal to abandon the option to develop the oil field. It can be seen from the table that the critical spot price (Sci) falls as the development costs decrease whereas it increases with increase in development costs. This is expected as a higher development costs would mandate higher probability of getting positive returns and consequently a higher value of spot price at the beginning of the development period.
Table 4.2 – Development Costs and Critical Spot Price The evolution of the value of the oil field in Stage I for the low and high values of development costs for multiple sets of spot prices has been shown in Fig 4.6 a and 4.6 b below. These can be compared the base case given in Fig. 4.5 
Fig 4.6 a 
Fig 4.6 b Download 0.67 Mb. Share with your friends:
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