Quick Start for:
Discounting Oil and Gas Income
Basis of the Manual
Introduction
Discounting
Discounted Cash Flow Appraisal
Discount Rate Components
Using the Three Techniques
Market Surveys
Developing a Discount Rate From Sales
Weighted Average Cost of Capital
Summary
Appendix 1: Discounted Cash Flow Method (Working Interest Portion Only)
Appendix 2: Estimation of Weighted Average Cost of Capital (WACC)
Appendix 3: Standard Deviation
Appendix 4: Property Specific Risk Factors
References
Appendix 3
Standard Deviation
The standard deviation is the square root of the average squared difference between the individual observations and the average value. The first step in the calculation of the standard deviation is to average the data arithmetically. The arithmetic average or "mean" value is denoted as z. An equation to calculate the mean value, z, of a data set is as follows:

z = 1/n(x1 + x2 + x3 + ... + xn)

where:

 z = mean value of a data set of n values x1 = unique value in data set n = total number of values in data set

The standard deviation, usually denoted by the symbol, S, would be calculated using the following equation:

S = (((x1 - z)2 + ... + (xn - z)2)/(n-1)).5

where:

 S = standard deviation of a data set with n values x1 = unique value in data set xn = nth value in data set n = total number in data set

Example: Procedure for calculating the standard deviation of a data set that has 10 sales with various internal rates of return (IRR).

 Sale No. IRR (%) (x - z) (x - z)^2 1 x1 11.0 -4.7 22.09 2 x2 25.0 9.3 86.49 3 x3 6.0 -9.7 94.09 4 x4 16.0 0.3 0.09 5 x5 16.0 0.3 0.09 6 x6 22.0 6.3 39.69 7 x7 9.0 -6.7 44.89 8 x8 14.0 -1.7 2.89 9 x9 13.0 -2.7 7.29 10 x10 25.0 9.3 86.49 157.0 384.10

Calculate the arithmetic average, z:
z = 157.0/10 = 15.7 IRR%

Calculate the standard deviation, S:
S = (384.1/(10-1)).5 = 6.5 IRR%

Range of 1 standard deviation
= 15.7 ± 6.5 = 9.2 < 15.7 < 22.2

Range of 2 standard deviations
= 15.7 ± 6.5(2) = 2.7 < 15.7 < 28.7

28.7%/year could be used as an upper limit to the discount rate range for high-risk properties.