Example Ⅰ Let's study an example of a petrochemical plant considering the production of a new petrochemical product. Its cash flow is:
Technical and Economic Evaluation Method and Application of Oil and Gas Industry (3rd Edition)
When the loan interest rate is assumed to be 1%, its NPV＝2.95 and IRR = 11%, both of which show that the project is barely acceptable. In order to estimate the accuracy of these methods, some settings must be made for the variability of cash flow values. Obviously, any situation should be dealt with according to its advantages and disadvantages. The following assumptions are only made on the basis of superficial rationality.
assumption 1: it is known that the cash flow in zero year is-15, pounds, with no error, which is essentially the input cost (advertising expenses, sample making expenses, etc.), and a clear budget has been made accordingly.
assumption 2: the remaining cash flows change randomly, where the Median is the value shown above, and it is assumed that the probability distribution of each cash flow is known (this is very important, because it is the key to the follow-up analysis and the content of our further discussion).
At present, some methods have been proposed to estimate these distributions, and the most commonly used method for continuous distribution seems to be the continuous distribution score point method. This method is essentially to quantify the opinions of the most experienced experts (appraisers). This method should first give the median value of unknown variables, that is, the possibility of being greater than or less than this value is equal. The first year's cash flow is about 4, pounds, and then only consider the probability that the cash flow is more than 4, pounds, and ask to estimate the "middle mark" of these results. For this estimate, the value is 6, pounds, which means that if all the information is known that the cash flow is more than 4, pounds, the chances of being more than or less than 6, pounds are equal. After careful consideration of these two benchmarks, the probability that the cash flow is greater than 6, pounds is 1/4. After a similar discussion on the low-value part of the other half's cash flow, another low-value "middle marker" will be obtained, namely 3, pounds. It is worth noting that there is no reason why the probability space between 3, pounds and 6, pounds is the same from the median of 4, pounds. Our brain can repeatedly search for the "middle point" in the four identified intervals, and will get cash flow values with probabilities of 1/8, 3/8, 5/8 and 7/8 respectively, and add them to the existing 1/4, 1/2 and 3/4 sequences.
finally, the assessor should decide to estimate the extreme value of cash flow-the best and worst cash flow values. This last step will be difficult, because people have different interpretations of "worst" and "best". The evaluator should be more careful to ensure that the extreme situations he can consider are reasonable and can't take absurd things into account. For example, all the competitors of the petrochemical plant closed down (at best) or a fire destroyed the petrochemical plant (at worst).
Based on this, it can be assumed that the first year's cash flow is as follows:
Technical and economic evaluation method and application of oil and gas industry (3rd edition)
Figure 7-13 is obtained by connecting the above data with a smooth curve with naked eyes. It should be noted that the actual cash flow may be composed of multiple expenditures and benefits, while the essential random variable may be the annual sales volume.
Figure 7-13 Subjective probability distribution of cash flow in the first year
Next, repeat the above process for cash flow in each year. This will be a time-consuming (especially for the same evaluator) and even exhausting process. An effective way to overcome this difficulty is to think that the probability distribution of cash flow in each subsequent year is completely a proportional replica of the first year. If this is acceptable, all that needs to be done is to estimate the median annual cash flow, just like the first year, which divides the interval and provides the scale factor. Table 7-6 can be obtained after all the data are processed.
Table 7-6 Cumulative Probability of Cash Flow
The generation process of each distribution value is as follows: a known distribution (year 1) is multiplied by the scale factors of 1.75, 1.5 and .5 respectively to get the distribution values of the second, third and fourth years. In practice, you can refer to a conversion table with random variables ranging from to 99. The values in this table are random variables that can be expressed as a function of 1 and the corresponding values in the cumulative probability diagram of cash flow in the first year (Figure 7-13). Therefore, the cash flow of the first year corresponding to the random variable with serial number 63 is 45.6. If the cash flow value of the third year corresponding to the same random number is found, the result should be 45.6× 1.5 = 68.4.
for a set of typical simulation values, the random numbers are 63, 17, 2 and 39, and the corresponding cash flows are 45.6(1 year), 46.2(2 years), 2.4(3 years) and 17.8(4 years), respectively, and the net present value is:
Technical and economic evaluation method and application of oil and gas industry In order to find out whether this is an abnormal result, a comprehensive simulation is needed. The IRR value of the above set of input data is -.7, which is not only lower than the loan interest rate but also negative. As the total income is less than the initial investment, this result should be predictable.
Some people may suggest that the assumptions in the above model are unrealistic, because the cash flows in any year are actually independent of each other. However, the actual situation is that if a project (in this case, the introduction of new petrochemical products) is successful, its cash flow will continue to be greater than the median cash flow, on the contrary, a mistake will lead to a low cash flow throughout the life of the project. In statistical terms, random variables are related, not independent. In the actual simulation, it is not difficult to deal with related problems. The problem lies in how to match the mathematical method with the concept understood by the evaluator. One way to solve this problem is to test the two extreme cases of complete independence and complete correlation, and think that the real situation should be somewhere in between, and hope that these extreme values will give the most reasonable values for any method to evaluate the feasibility of the project and help to make decisions.
we have considered a completely independent model. Assuming a completely related model, each cash flow variable is in the same position relative to its distribution. This can be done by using the simple method of using the same random number for each group of variables X1, X2, X3 and X4. For example, if we use random number 63, the corresponding cash flows are 45.6, 79.8, 68.4 and 22.8, respectively, and NPV＝24.4 and IRR = 17.8%.
we simulated both independent and correlated hypothetical models, and plotted the results in the form of cumulative probability of NPV and IRR (Figure 7-14, Figure 7-15).
Figure 7-14 NPV Cumulative Probability Diagram
Figure 7-15/RR Cumulative Probability Diagram
For related models, these two criteria have changed greatly than expected. This is because in this model, the effect of extreme random variables is repeated four times, while in the independent model, the effect of extreme values tends to be slowed down by the other three random variables. Further observation shows that the curves of the related models are similar in shape and similar to the usual cumulative probability curve of cash flow (Figure 7-13). This phenomenon can be simply explained as: for any random variable, there is a unique cash flow in four years, so there will be a unique NPV and IRR. The probability expressions of cash flow, NPV and IRR are obviously related, but in fact they don't need to be simulated.
when evaluating the feasibility of a project with these diagrams, the decision maker may first notice that the probability of NRV being negative is between .34 and .48, both of which may be unacceptably high. Similarly, the probability that IRR is less than the loan interest rate (1%) also has a range, and the same conclusion can be drawn. These figures will bring us deeper thinking, for example, the risk of negative NPV may be offset by a large number of positive values.
the judgment standard of payback period of investment is not involved in the above simulation process, although this method will not cause difficulties in analysis. As mentioned above, the values of the relevant models can be directly obtained, and the results are shown in Table 7-7.
the combination of investment model establishment and simulation provides a powerful tool for the evaluation of project feasibility, which provides a detailed analysis of the risks involved for decision makers on the basis of the initial subjective probability provided by professional appraisers. In this sense, it has the most useful information, and the risks can't be completely avoided, but they are completely exposed.
Table 7-7 Cumulative Probability
Example II Oil production is a complex system composed of underground oil resources, reserves, output and investment. In the petroleum production system, reserves are the key element to link exploration, development and exploitation. The reserves found through exploration activities can only realize its value through oil and gas exploitation, and enterprises can obtain economic benefits, thus maintaining the continuity and stability of the petroleum production system.
in the petroleum production system, the capital flow may present various operation modes. Figure 7-16 shows the discounted net cash flow and the accumulated discounted net cash flow in the same time series, and points A, B, C, D and E respectively show their characteristic points. This is a typical capital flow curve.
the essence of economic recoverable reserves evaluation is to determine these characteristic points on the capital flow curve. Point C is the critical point of economic benefits of reserves development, which is of great significance to the development and utilization of unexploited reserves. After the production enters the declining period, the discounted net cash flow drops to zero and the cumulative discounted net cash flow rises to the maximum. Therefore, point E is the highest point of economic benefits that can be achieved by reserve development.
from the above analysis, it can be seen that the evaluation of economically recoverable reserves is dynamic and staged, which runs through the whole process of oil production. The evaluation of economically recoverable reserves is based on the analysis of capital flow in a certain period in the future, to predict all the annual trends of capital outflow and inflow in the oil production system, to ensure that the country and the exploration, development and production departments get corresponding profits under certain technical and economic conditions, so as to determine the economic benefits and economic development boundaries of reserve development.
in the cash flow statement, when the cumulative discounted net cash flow reaches the maximum positive value and the discounted net cash flow is equal to zero, it is called zero benefit. For the old oil field under development, if the calculated cash flow statement has no economic benefit in the initial year of evaluation, it shows that the oil field has been exploited in a state of zero benefit loss. For a new oilfield, point C in Figure 7-16 is the critical point where reserves can be exploited and economic benefits can be obtained. If the cumulative discounted net cash flow is always negative from the evaluation start year, although the discounted net cash flow has risen to a positive value, it shows that there is still no economic benefit from reserves development in this oilfield at present. Otherwise, the cumulative oil production from the initial year of evaluation to the zero-benefit year is the (remaining) economically recoverable reserves, and the net present value NPV is the value of the (remaining) economically recoverable reserves, and its expression is as follows:
Figure 7-16 Typical economic characteristics of oil production
Technical and economic evaluation method and application of oil and gas industry (3rd edition)
Where NPV is the value of the (remaining) economically recoverable reserves. CIi is the cash inflow in the first year; COi is the cash outflow in the first year; IR is the target internal rate of return; T is the economic mining life.
the cash flow method comprehensively reflects the dynamic changes of various factors affecting the economically recoverable reserves in the oil production system, and takes into account the time value of funds, so it is applicable to all oil fields. However, because this method is based on oil production prediction, the prediction accuracy will affect the evaluation results. Therefore, in practical application, the prediction method should be reasonably selected according to the types of reserves, development methods and production stages. In addition, the economic limit method needs fewer parameters, its calculation formula is simple and convenient, and it can avoid the influence caused by the forecast deviation of various development and production indicators. However, this method is highly sensitive to parameters and cannot calculate most of the required evaluation indicators, so it can only be used as an auxiliary method for the evaluation of economically recoverable reserves.