# USING A SIMULATION MODEL TO PLAN PROPERTY ACQUISITIONS: EVALUATION VS. BID PRACTICES

John R. SchuylerConsultant

Aurora, Colo.

Making profitable acquisitions in a competitive environment is difficult. This is because the winning bidders often pay more than the property is worth. This paper shows how to measure the important impacts of different valuation and bidding strategies: improving engineering estimates, adjusting bid fractions, and modifying reserve category risk adjustments. A less complex model is used to optimize the bid for a single acquisition.

### OBJECTIVE/DECISION RULE

As with the exploration model, the objective is to maximize the net worth of the company at the end of the planning horizon. In acquiring properties, the variable most under control is bid fraction or bid level. That times the value estimate, the bid value, equals the bid amount.

Assume that acquisitions are 100% financed at our incremental after-tax cost of capital. Assume, further, that our parameter estimates are 100% accurate. Then our bid value is the amount we could pay for a property and exactly break even.

### MODEL ASSUMPTIONS

The full company model is a fairly detailed representation of an example company. The essential features of existing and added production, inflation, bank financing, income taxes, etc. are expressed in the formulas. Interested persons may contact the author to obtain a full list of assumptions.

The model allows one to experiment with alternate decision policies. The full company portfolio model is required because an optimum decision for a single investment is different from the optimum decision when considered in the context of a series of investment opportunities. This important point is demonstrated later with a single-acquisition model.

E. C. Capen, et. al. (1968), provide an excellent discussion about the competitive effect for lease bidding in frontier areas. They show that bid fractions should be lowered as the evaluation uncertainties increase and as the number of competitors increases.

The author uses a simple competition model. Each represented competitor goes through the same process to determine bid values. Our average error in estimating initial production and decline rate can be the same or different from the competition. Our bid fraction may also be different from our competitors.

He used the same portfolio of properties as developed for the exploration model. The chance of discovery and testwell cost parameters obviously no longer apply. Tables 1 and 2 summarize the typical properties. The development costs shown are for 100% undeveloped reserves, although the properties are actually in various stages of development. The Cost Components column in Table 2 shows the fraction of the development costs that are applied to the respective reserves. Variable costs include both lifting costs and production taxes.

The prospect input assumptions are expected values. That is, the average production realized will equal the average production forecast. The Risk Adjustment column in Table 2 shows value adjustments to reserve categories. As is common is our industry, these adjustments are used to reduced value estimates for lesser reserve categories. The impact of this conservative practice, reflecting a risk-averse attitude, is one of effects the model was used to test.

The author assumed that the company meets five competitors at each property sale. He further assumes that each competitor uses a 75% bid fraction in preparing the bid. As with the exploration model, the major uncertainties are initial production, production decline rate, and forecasts of prices and inflation. Reserve values are computed using the then-current oil price, the long-term price trend, and a random component. Each company has judgment errors for initial production and decline rate distributed about the mean values. With equal bid fractions and reserve category adjustments, the company with the most optimistic reserve estimate will bid highest and win the sale.

### RESULTS FROM THE FULL COMPANY MODEL

Table 3 summarizes the results shown on the first two graphs, Fig. 1 and Fig. 2.

Fig. 1 shows the base case and several reference cases. This is a cumulative frequency type curve showing the probability that the amount will be greater than or equal to the x-axis value. "Determined price and inflation" refers to using the base escalations without the random fluctuations. The volatility in prices and inflation causes perhaps half the variance in the base case and is responsible for the extremes. The no-bid, "do nothing" cases provide benchmarks for evaluating the success of the acquisition programs. Note that many times the "no bid" strategy outperforms the acquisitions strategy.

The high trial for the base case had a $186 million ending net worth. There were 23 acquisitions which increased value approximately $45 million at the then-current oil prices. More than $116 million of value was added due to increasing prices: oil prices for the fourth year were $53/bbl. To better reflect reality, future versions of this model will have a likely "windfall profits" tax which would absorb much of any major price improvement.

Fig. 2 shows the results of four analysis and bidding strategies. The curves are from four strategies applied to 30 different price x inflation x sale portfolio scenarios. Reducing the base error 50% provides the greatest improvement, $4.1 million, or 13%, over the base case. Many companies might achieve this error reduction with minimal cost, such as by using techniques to refine and eliminate biases from professional judgements.

Risk adjusting or discounting lower reserve categories (factors in Table 2) introduces a conservative bias into the analysis. The author expected, therefore, that not making reserve category adjustments would improve value estimates and lead to improved financial performance. He was surprised that the "no category risk" case was worse. This can be explained by recalling (1) the most optimistic bidder has the greatest chance of overpaying for a property and (2) lower reserve categories have the greatest uncertainties. Thus, bid fractions should be lowered as the competition or reserve uncertainties increase. This finding appears to validate the industry practice of risking reserve categories. However, this is a case where the right adjustment, at least in direction, is being made for the wrong reason. In his model assumptions, the benefit of more-objectively assessing value is overshadowed by the competitive situation. With simulation, we have a tool to replace indiscriminate rules-of-thumb with an objective analysis that incorporates our beliefs and best judgments.

Another surprise in the model was finding that increasing our bid fraction (from .75 to .80) resulted in better results than did a decrease in this parameter. The opposite was expected. It was interesting to track down the cause. In general, the 75% bid fraction provides favorable profits for property acquisitions in the situation modeled. Normally, one expects to get even better results by bidding lower and more often. However, the author assumed only 50 properties would be offered for sale each year. About 12% of the base case trial-years fail to spend substantially all the budget amounts. The unused budget earns interest or is applied to retiring debt, with a lower return than acquiring properties. For the assumptions used, the slight increase in our bid fraction was able to make additional and still profitable - acquisitions by being more aggressive.

### A SINGLE SALE MODEL

The author developed another simulation model to test strategies for a single property acquisition. The objective is to determine the best value of our bid fraction for the given situation. Experiments with this model provide some valuable insights into the bidding problem. It is important to note that the one-sale and multiple-sale problems are different and have different optimum bid fractions.

In using the program, one enters values for 16 parameters, describing the economic environment, sale property, and competition. Four of these variables are represented by probability distributions. The parameters for the competitors' reserve evaluations and bid fractions are determined from sampling the respective probability distributions.

Figs. 3 to 6 show example results from using this model. With the assumptions he used, the true property values average $28 million. The Five Sale simulations approximate the situation where one expects to have about five opportunities to make a single property acquisition. The number of opportunities times the average sale amount should approximately equal the expected property sales in this value range during the planning horizon.

The Single Sale simulations can be used to determine the optimum bid fraction when there is only one acquisition opportunity or when we have, for practical purposes, unlimited available capital.

Figs. 3 and 4 show expected value surfaces as functions of our bid fraction and mean competitors' bid fraction. The heavy trace line shows approximately where our optimum bid fraction values lie along the ridge crest. It is remarkable that, for the property and economics parameters used, our optimum bid fractions vary little across a broad range of competitor bid fractions, and between the single- and five-sale cases.

The author was surprised at the low slope near the optimums. However, small improvements are very valuable. A correction of .05 in our bid fraction is worth about $350,000 to the subject company. Other trials with smaller uncertainties in reserves, pricing, and competitor bid fractions provide greater surface relief, greater range in our optimum bid fraction, and higher expected profits at the optimums.

Figs. 5 and 6 show expected results when we use our optimum bid fractions. As one expects, we enjoy higher expected values and higher acquisition success rates when given multiple opportunities.

### DISCUSSION

The number of competitors, the quality of their evaluation engineering, and their strategies are important parameters when bidding for proved reserve leases. The full company simulation model provides a way to plan a property acquisition program, to evaluate very major acquisitions, and to test alternate general decision strategies. A single-acquisition model is more useful for analyzing routine, individual sales.

A simulation model, whether it represents the entire company, one business unit, or a specific transaction can provide important benefits. All the important attitudes and judgments can be incorporated, providing a logical and consistent way to make the best decision. The modeling process, itself, provides valuable insights. And it provides a low-cost way to measure the impact of different conditions and to test alternative strategies.

### ACKNOWLEDGMENTS

The author gratefully acknowledges the contribution of Dr. John A. Pederson in reviewing a draft of this article. The author bears full responsibility for the integrity of the data and models.

### BIBLIOGRAPHY

Capen, E. C., Clapp, R. V., and Campbell, W. M, 1971, Joumat of Petroleum Technology, June 1971, pp. 641-653.

*Copyright 1990 Oil & Gas Journal. All Rights Reserved.*