Rapid Present-Worth Evaluations for Oil- and Gas-Producing Properties

Abstract

Introduction A method for rapid evaluation of the present worth of oil- and gas-producing properties has been developed. This method separately evaluates the present worth of estimated income, expense and depreciation, and combines these separate evaluations to find the present worth of future retained cash after income tax. Calculations may be made by slide rule and without the usual, lengthy columnar tabulations. The method does not apply to properties on which income tax is calculated through cost depletion. Although only constant rate and constant-per cent-decline rates are considered here, the basic method can be readily adapted to harmonic and hyperbolic decline rates. Separate evaluations of the present worth of income, expenses and depreciation are made by the use of deferment factors which apply to the total value during any period in which money is received (or spent) at a constant rate or at constant-per cent-decline rates. These deferment factors determine the present worth of income during a period at the beginning of that period, and additional (lump-sum) factors are applied to determine the present worth at any time before the beginning of the period. Present Worth of Future Production For example, it is estimated that a well will produce 91,250 bbl at 50 BOPD (five years), and 97,500 bbl at constant-per cent-decline rates (50 BOPD to 3 BOPD for an additional 16 years). The sales price of oil is estimated at $3.00/bbl over the entire 21-year period, and a 10 per cent discount factor is to be used. To find the present worth of this production, divide the total time into two periods-a five-year constant-rate period and a 16-year constant-per cent-decline period. For the five-year period, it is necessary to find only a single deferment factor. This may be found on Fig. 1-A by calculating a Tj value and finding the intercept on the "constant-rate" curve: T = time in years = 5; j = nominal interest rate = .10; Tj = (5)(.10) = .5; Deferment Factor (Fig. 1-A) = .787. The present worth of the first five year's production at the beginning of the first year is (91,250 bbl) ($3.00/bbl) (.787) = $215,000. For the 16-year constant-per cent-decline period, an additional value (r) must be found and used as follows: r = initial rate/final rate = 50 BOPD/3 BOPD = 16.67; Tj = (16 years)(.10) = 1.6; at Tj = 1.6 and r = 16.67 (Fig. 1-B), Deferment Factor = .667. The present worth at the end of the fifth year (beginning of the 16-year period) is (91,500 bbl) ($3.00/bbl) (.667) = $195,000. To find the present worth of the 16 year's production at the beginning of the first year (i.e., five full years before the beginning of the 16-year period), an additional deferment factor is necessary: Tj = (5years)(.10) = .5; at .5 Tj on Fig. 1-A, Lump-sum Deferment Factor = .605. Present value five years before beginning of 16-year period is ($195,000)(.605) = $118,000. The total present worth of the entire 21 years of production is then $215,000 + $118,000 = $333,000. In a similar manner, it is possible to determine the present worth of any schedule of expenses composed of constant-rate or constant-percent-decline-rate periods. The present worth of the expenses may then be subtracted from the present worth of income to find the present worth of the net income (gross income minus expenses). Cash Retained After Income Taxes To calculate the present worth of cash retained after income tax, it is necessary to also calculate present worth of a depreciation schedule and to adjust the present worth of income, expense and depreciation before adding together-in order to compensate for income tax. JPT P. 1075^