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Economics: time value of money (view source)

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==Present value==
 
==Present value==
 +
 +
[[File:Rose_time-value-of-money_1.png|300px|thumb|'''Figure 1.''' Comparison of project cash flows and equivalent present value.]]
    
This same equation can be rearranged to solve for the equivalence (or present value) of a future sum of money (such as a project net cash flow) received some time in the future. For example, a dollar that we expect to receive one, two, and three years hence is worth today $0.909, $0.826, and $0.751, respectively, if the time value of money is 10% per year compounded annually. This equation expresses this principle of present value:
 
This same equation can be rearranged to solve for the equivalence (or present value) of a future sum of money (such as a project net cash flow) received some time in the future. For example, a dollar that we expect to receive one, two, and three years hence is worth today $0.909, $0.826, and $0.751, respectively, if the time value of money is 10% per year compounded annually. This equation expresses this principle of present value:
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:<math>P = \frac{F}{(1 + i)^t}</math>
 
:<math>P = \frac{F}{(1 + i)^t}</math>
   −
[[File:Rose_time-value-of-money_1.jpg|thumb|Comparison of project cash flows and equivalent present value.]]
+
The present value concept is important in [[petroleum]] economics because we need to know how to place a value on cash flows to be received from production in future years. This concept is demonstrated in [[:Image:Rose_time-value-of-money_1.jpg|Figure 1]]. In oil and gas property evaluation, profit is measured in terms of net cash inflows and net cash outflows. In the figure, the horizontal line represents time, the vertical arrows above the horizontal line represent net cash inflows, and the vertical arrows below the horizontal line represent net cash outflows. The profit is usually measured for increments of one year. One exception is the time 0 profit period. Time 0 is the instant in time when the first significant expenditure is made.
−
The present value concept is important in petroleum economics because we need to know how to place a value on cash flows to be received from production in future years. This concept is demonstrated in the figure. In oil and gas property evaluation, profit is measured in terms of net cash inflows and net cash outflows. In the figure, the horizontal line represents time, the vertical arrows above the horizontal line represent net cash inflows, and the vertical arrows below the horizontal line represent net cash outflows. The profit is usually measured for increments of one year. One exception is the time 0 profit period. Time 0 is the instant in time when the first significant expenditure is made.
      
When each of the future net cash flows are discounted to time 0 using the present value equation, the resulting net cash flow is called the ''net present value'' and is equivalent to the project cash flows at the assumed discount rate. The equivalent time 0 net cash flow is also shown in the figure.
 
When each of the future net cash flows are discounted to time 0 using the present value equation, the resulting net cash flow is called the ''net present value'' and is equivalent to the project cash flows at the assumed discount rate. The equivalent time 0 net cash flow is also shown in the figure.
    
==Discount rates==
 
==Discount rates==
−
[[File:table_rose_time-value-of-money_1.jpg|thumb|Present value factors]]
+
 
−
The table shows present value factors at different interest rates (or ''discount rates'') in future years. Some corporations use a discount rate approximately equal to the corporate cost of capital, or the present inflation rate, plus an additional 3-4% (which represents "real" bank interest). At the time this paper was written, this gave an 8-9% [[corporate discount rate]]. During this time, however, most U.S. companies were using a discount rate of 12-15%, and international firms were using 15-18%.
+
Table 1 shows present value factors at different interest rates (or ''discount rates'') in future years. Some corporations use a discount rate approximately equal to the corporate cost of capital, or the present inflation rate, plus an additional 3-4% (which represents "real" bank interest). At the time this paper was written, this gave an 8-9% [[corporate discount rate]]. During this time, however, most U.S. companies were using a discount rate of 12-15%, and international firms were using 15-18%.
 +
 
 +
{| class = "wikitable"
 +
|-
 +
|+ {{table number|1}}Present value factors
 +
|-
 +
! Years Hence
 +
! 1%
 +
! 3%
 +
! 4%
 +
! 5%
 +
! 6%
 +
! 8%
 +
! 10%
 +
! 12%
 +
! 15%
 +
! 20%
 +
! 30%
 +
! 40%
 +
! 50%
 +
|-
 +
| 1
 +
| 0.990
 +
| 0.971
 +
| 0.962
 +
| 0.952
 +
| 0.943
 +
| 0.926
 +
| 0.909
 +
| 0.893
 +
| 0.870
 +
| 0.833
 +
| 0.769
 +
| 0.714
 +
| 0.667
 +
|-
 +
| 2
 +
| 0.980
 +
| 0.943
 +
| 0.925
 +
| 0.907
 +
| 0.890
 +
| 0.857
 +
| 0.826
 +
| 0.797
 +
| 0.756
 +
| 0.694
 +
| 0.592
 +
| 0.510
 +
| 0.444
 +
|-
 +
| 3
 +
| 0.971
 +
| 0.915
 +
| 0.889
 +
| 0.864
 +
| 0.840
 +
| 0.794
 +
| 0.751
 +
| 0.712
 +
| 0.658
 +
| 0.579
 +
| 0.455
 +
| 0.364
 +
| 0.296
 +
|-
 +
| 4
 +
| 0.961
 +
| 0.888
 +
| 0.855
 +
| 0.823
 +
| 0.792
 +
| 0.735
 +
| 0.683
 +
| 0.636
 +
| 0.572
 +
| 0.482
 +
| 0.350
 +
| 0.260
 +
| 0.198
 +
|-
 +
| 5
 +
| 0.951
 +
| 0.863
 +
| 0.822
 +
| 0.784
 +
| 0.747
 +
| 0.681
 +
| 0.621
 +
| 0.567
 +
| 0.497
 +
| 0.402
 +
| 0.269
 +
| 0.186
 +
| 0.132
 +
|-
 +
| 6
 +
| 0.942
 +
| 0.837
 +
| 0.790
 +
| 0.746
 +
| 0.705
 +
| 0.630
 +
| 0.564
 +
| 0.507
 +
| 0.432
 +
| 0.335
 +
| 0.207
 +
| 0.133
 +
| 0.088
 +
|-
 +
| 7
 +
| 0.933
 +
| 0.813
 +
| 0.760
 +
| 0.711
 +
| 0.665
 +
| 0.583
 +
| 0.513
 +
| 0.452
 +
| 0.376
 +
| 0.279
 +
| 0.159
 +
| 0.095
 +
| 0.059
 +
|-
 +
| 8
 +
| 0.923
 +
| 0.789
 +
| 0.731
 +
| 0.677
 +
| 0.627
 +
| 0.540
 +
| 0.467
 +
| 0.404
 +
| 0.327
 +
| 0.233
 +
| 0.123
 +
| 0.068
 +
| 0.039
 +
|-
 +
| 9
 +
| 0.914
 +
| 0.766
 +
| 0.703
 +
| 0.645
 +
| 0.592
 +
| 0.500
 +
| 0.424
 +
| 0.361
 +
| 0.284
 +
| 0.194
 +
| 0.094
 +
| 0.048
 +
| 0.026
 +
|-
 +
| 10
 +
| 0.905
 +
| 0.744
 +
| 0.676
 +
| 0.614
 +
| 0.558
 +
| 0.463
 +
| 0.386
 +
| 0.322
 +
| 0.247
 +
| 0.162
 +
| 0.073
 +
| 0.035
 +
| 0.017
 +
|-
 +
| 11
 +
| 0.896
 +
| 0.722
 +
| 0.650
 +
| 0.585
 +
| 0.527
 +
| 0.429
 +
| 0.350
 +
| 0.287
 +
| 0.215
 +
| 0.135
 +
| 0.056
 +
| 0.025
 +
| 0.012
 +
|-
 +
| 12
 +
| 0.887
 +
| 0.701
 +
| 0.625
 +
| 0.557
 +
| 0.497
 +
| 0.397
 +
| 0.319
 +
| 0.257
 +
| 0.187
 +
| 0.112
 +
| 0.043
 +
| 0.018
 +
| 0.008
 +
|-
 +
| 13
 +
| 0.879
 +
| 0.681
 +
| 0.601
 +
| 0.530
 +
| 0.469
 +
| 0.368
 +
| 0.290
 +
| 0.229
 +
| 0.163
 +
| 0.093
 +
| 0.033
 +
| 0.013
 +
| 0.005
 +
|-
 +
| 14
 +
| 0.870
 +
| 0.661
 +
| 0.577
 +
| 0.505
 +
| 0.442
 +
| 0.340
 +
| 0.263
 +
| 0.205
 +
| 0.141
 +
| 0.078
 +
| 0.025
 +
| 0.009
 +
| 0.003
 +
|-
 +
| 15
 +
| 0.861
 +
| 0.642
 +
| 0.555
 +
| 0.481
 +
| 0.417
 +
| 0.315
 +
| 0.239
 +
| 0.183
 +
| 0.123
 +
| 0.065
 +
| 0.020
 +
| 0.006
 +
| 0.002
 +
|-
 +
| 16
 +
| 0.853
 +
| 0.623
 +
| 0.534
 +
| 0.458
 +
| 0.394
 +
| 0.292
 +
| 0.218
 +
| 0.163
 +
| 0.107
 +
| 0.054
 +
| 0.015
 +
| 0.005
 +
| 0.002
 +
|-
 +
| 17
 +
| 0.844
 +
| 0.605
 +
| 0.513
 +
| 0.436
 +
| 0.371
 +
| 0.270
 +
| 0.198
 +
| 0.146
 +
| 0.093
 +
| 0.045
 +
| 0.012
 +
| 0.003
 +
| 0.001
 +
|-
 +
| 18
 +
| 0.836
 +
| 0.587
 +
| 0.494
 +
| 0.416
 +
| 0.350
 +
| 0.250
 +
| 0.180
 +
| 0.130
 +
| 0.081
 +
| 0.038
 +
| 0.009
 +
| 0.002
 +
| 0.001
 +
|-
 +
| 19
 +
| 0.828
 +
| 0.570
 +
| 0.475
 +
| 0.396
 +
| 0.331
 +
| 0.232
 +
| 0.164
 +
| 0.116
 +
| 0.070
 +
| 0.031
 +
| 0.007
 +
| 0.002
 +
| 0.000
 +
|-
 +
| 20
 +
| 0.820
 +
| 0.554
 +
| 0.456
 +
| 0.377
 +
| 0.312
 +
| 0.215
 +
| 0.149
 +
| 0.104
 +
| 0.061
 +
| 0.026
 +
| 0.005
 +
| 0.001
 +
|
 +
 
 +
|-
 +
| 21
 +
| 0.811
 +
| 0.538
 +
| 0.439
 +
| 0.359
 +
| 0.294
 +
| 0.199
 +
| 0.135
 +
| 0.093
 +
| 0.053
 +
| 0.022
 +
| 0.004
 +
| 0.001
 +
|
 +
 
 +
|-
 +
| 22
 +
| 0.803
 +
| 0.522
 +
| 0.422
 +
| 0.342
 +
| 0.278
 +
| 0.184
 +
| 0.123
 +
| 0.083
 +
| 0.046
 +
| 0.018
 +
| 0.003
 +
| 0.001
 +
|
 +
 
 +
|-
 +
| 23
 +
| 0.795
 +
| 0.507
 +
| 0.406
 +
| 0.326
 +
| 0.262
 +
| 0.170
 +
| 0.112
 +
| 0.074
 +
| 0.040
 +
| 0.015
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 24
 +
| 0.788
 +
| 0.492
 +
| 0.390
 +
| 0.310
 +
| 0.247
 +
| 0.158
 +
| 0.102
 +
| 0.066
 +
| 0.035
 +
| 0.013
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 25
 +
| 0.780
 +
| 0.478
 +
| 0.375
 +
| 0.295
 +
| 0.233
 +
| 0.146
 +
| 0.092
 +
| 0.059
 +
| 0.030
 +
| 0.010
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 26
 +
| 0.772
 +
| 0.464
 +
| 0.361
 +
| 0.281
 +
| 0.220
 +
| 0.135
 +
| 0.084
 +
| 0.053
 +
| 0.026
 +
| 0.009
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 27
 +
| 0.764
 +
| 0.450
 +
| 0.347
 +
| 0.268
 +
| 0.207
 +
| 0.125
 +
| 0.076
 +
| 0.047
 +
| 0.023
 +
| 0.007
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 28
 +
| 0.757
 +
| 0.437
 +
| 0.333
 +
| 0.255
 +
| 0.196
 +
| 0.116
 +
| 0.069
 +
| 0.042
 +
| 0.020
 +
| 0.006
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 29
 +
| 0.749
 +
| 0.424
 +
| 0.321
 +
| 0.243
 +
| 0.185
 +
| 0.107
 +
| 0.063
 +
| 0.037
 +
| 0.017
 +
| 0.005
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 30
 +
| 0.742
 +
| 0.412
 +
| 0.308
 +
| 0.231
 +
| 0.174
 +
| 0.099
 +
| 0.057
 +
| 0.033
 +
| 0.015
 +
| 0.004
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 31
 +
| 0.735
 +
| 0.400
 +
| 0.296
 +
| 0.220
 +
| 0.164
 +
| 0.092
 +
| 0.052
 +
| 0.030
 +
| 0.013
 +
| 0.004
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 32
 +
| 0.727
 +
| 0.388
 +
| 0.285
 +
| 0.210
 +
| 0.155
 +
| 0.085
 +
| 0.047
 +
| 0.027
 +
| 0.011
 +
| 0.003
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 33
 +
| 0.720
 +
| 0.377
 +
| 0.274
 +
| 0.200
 +
| 0.146
 +
| 0.079
 +
| 0.043
 +
| 0.024
 +
| 0.010
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 34
 +
| 0.713
 +
| 0.366
 +
| 0.264
 +
| 0.190
 +
| 0.138
 +
| 0.073
 +
| 0.039
 +
| 0.021
 +
| 0.009
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 35
 +
| 0.706
 +
| 0.355
 +
| 0.253
 +
| 0.181
 +
| 0.130
 +
| 0.068
 +
| 0.036
 +
| 0.019
 +
| 0.008
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 36
 +
| 0.699
 +
| 0.345
 +
| 0.244
 +
| 0.173
 +
| 0.123
 +
| 0.063
 +
| 0.032
 +
| 0.017
 +
| 0.007
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 37
 +
| 0.692
 +
| 0.335
 +
| 0.234
 +
| 0.164
 +
| 0.116
 +
| 0.058
 +
| 0.029
 +
| 0.015
 +
| 0.006
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 38
 +
| 0.685
 +
| 0.325
 +
| 0.225
 +
| 0.157
 +
| 0.109
 +
| 0.054
 +
| 0.027
 +
| 0.013
 +
| 0.005
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 39
 +
| 0.678
 +
| 0.316
 +
| 0.217
 +
| 0.149
 +
| 0.103
 +
| 0.050
 +
| 0.024
 +
| 0.012
 +
| 0.004
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 40
 +
| 0.672
 +
| 0.307
 +
| 0.208
 +
| 0.142
 +
| 0.097
 +
| 0.046
 +
| 0.022
 +
| 0.011
 +
| 0.004
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 41
 +
| 0.665
 +
| 0.298
 +
| 0.200
 +
| 0.135
 +
| 0.092
 +
| 0.043
 +
| 0.020
 +
| 0.010
 +
| 0.003
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 42
 +
| 0.658
 +
| 0.289
 +
| 0.193
 +
| 0.129
 +
| 0.087
 +
| 0.039
 +
| 0.018
 +
| 0.009
 +
| 0.003
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 43
 +
| 0.652
 +
| 0.281
 +
| 0.185
 +
| 0.123
 +
| 0.082
 +
| 0.037
 +
| 0.017
 +
| 0.008
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 44
 +
| 0.645
 +
| 0.272
 +
| 0.178
 +
| 0.117
 +
| 0.077
 +
| 0.034
 +
| 0.015
 +
| 0.007
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 45
 +
| 0.639
 +
| 0.264
 +
| 0.171
 +
| 0.111
 +
| 0.073
 +
| 0.031
 +
| 0.014
 +
| 0.006
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 46
 +
| 0.633
 +
| 0.257
 +
| 0.165
 +
| 0.106
 +
| 0.069
 +
| 0.029
 +
| 0.012
 +
| 0.005
 +
| 0.002
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 47
 +
| 0.626
 +
| 0.249
 +
| 0.158
 +
| 0.101
 +
| 0.065
 +
| 0.027
 +
| 0.011
 +
| 0.005
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 48
 +
| 0.620
 +
| 0.242
 +
| 0.152
 +
| 0.096
 +
| 0.061
 +
| 0.025
 +
| 0.010
 +
| 0.004
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 49
 +
| 0.614
 +
| 0.235
 +
| 0.146
 +
| 0.092
 +
| 0.058
 +
| 0.023
 +
| 0.009
 +
| 0.004
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|-
 +
| 50
 +
| 0.608
 +
| 0.228
 +
| 0.141
 +
| 0.087
 +
| 0.054
 +
| 0.021
 +
| 0.009
 +
| 0.003
 +
| 0.001
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|
 +
 
 +
|}
    
Some corporations advocate calculating an average [[reinvestment opportunity rate]] based on past performance and using this discount rate. When the historical record is analyzed (sometimes called a ''post audit''), the analysis can be done on both a dollars-of-the-day basis and in terms of constant purchasing power dollars. It is not an easy task to put all the project cash flows in terms of constant purchasing power for the "basket of goods" the corporation purchases. The concept of using the future price or cost increases of the capital goods purchased by the corporation as an index for loss of purchasing power is discussed in a paper by Krasts and Henkel<ref>Krasts, A., and T. Henkel, 1977, Effect of inflation on discounted cash flow rates of return: Managerial Planning, Nov/Dec, p. 21-26</ref>, in which they apply the concept to discounted cash flow rate of return (DCFROR) calculations. When the post audit average constant purchasing power rate of return is used as the discount rate in net present value calculations, the effect is that projects are compared assuming treasury growth. The project cash flows must also be in terms of constant purchasing power.
 
Some corporations advocate calculating an average [[reinvestment opportunity rate]] based on past performance and using this discount rate. When the historical record is analyzed (sometimes called a ''post audit''), the analysis can be done on both a dollars-of-the-day basis and in terms of constant purchasing power dollars. It is not an easy task to put all the project cash flows in terms of constant purchasing power for the "basket of goods" the corporation purchases. The concept of using the future price or cost increases of the capital goods purchased by the corporation as an index for loss of purchasing power is discussed in a paper by Krasts and Henkel<ref>Krasts, A., and T. Henkel, 1977, Effect of inflation on discounted cash flow rates of return: Managerial Planning, Nov/Dec, p. 21-26</ref>, in which they apply the concept to discounted cash flow rate of return (DCFROR) calculations. When the post audit average constant purchasing power rate of return is used as the discount rate in net present value calculations, the effect is that projects are compared assuming treasury growth. The project cash flows must also be in terms of constant purchasing power.
Line 43: Line 904:     
==See also==
 
==See also==
−
* [[Expected value and chance of success]]
+
* [[Risk: expected value and chance of success]]
−
* [[Building a cash flow model]]
+
* [[Cash flow model]]
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* [[About taxes]]
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* [[Taxes]]
−
* [[Key economic parameters]]
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* [[Economics: key parameters]]
      −
[[Category:Economics and risk assessment]][[Category:Pages with unformatted tables]][[Category:Test content]]
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[[Category:Economics and risk assessment]][[Category:Test content]]
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[[Category:Methods in Exploration 10]]
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