Intrinsic value of Navigant Consulting - NCI

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$23.13

  Intrinsic Value

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  Rating & Target

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  Value-price divergence*

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Previous close

$23.13

 
Intrinsic value

$50.37

 
Up/down potential

+118%

 
Rating

str. buy

 
Value-price divergence* premium content

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*Intrinsic value change (in %) minus stock price change (in %) in the past 12 months.

We calculate the intrinsic value of NCI stock by summing up the current values of future distributable cash flows generated by the company and dividing the sum by the number of outstanding shares. As such, the intrinsic value calculation depends entirely on projections. The more accurate your projections of the company's performance are - the more reliable is the intrinsic value calculation result. Please make sure to check the stock valuation input data below and adjust it if necessary. The quality of the output (intrinsic valuation result) is only as good as the quality of the input. See also DISCLAIMERS.

STOCK VALUATION INPUT DATA

Revenue (in 2016), $M
Initial revenue growth rate, %
Terminal revenue growth rate, %
Revenue decline factor
Initial discount rate, %
Discount rate multiplier
Variable cost ratio, %
Fixed operating expenses, $M
Interest rate on debt, %
Effective corporate tax rate, %
Production assets / Revenue, %
Life of production assets, yrs
Working capital / Revenue, %
Revenue / Adjusted assets
Adjusted equity ratio
Cash flow adjustment, % of Revenue
Book value of equity, $M
Shares outstanding, mln
Market capitalization, $bln 1.1

 

FINANCIAL STATEMENTS FORECAST and PRESENT VALUE CALCULATION

Fiscal year
2016(a)
   2017
   2018
   2019
   2020
   2021
   2022
   2023
   2024
   2025
   2026
   2027
   2028
   2029
   2030
   2031
   2032
   2033
   2034
   2035
   2036
   2037
   2038
   2039
   2040
   2041
   2042
   2043
   2044
   2045
   2046

INCOME STATEMENT

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Revenue growth rate, %
  12.51
  14.20
  13.28
  12.45
  11.71
  11.04
  10.43
  9.89
  9.40
  8.96
  8.56
  8.21
  7.89
  7.60
  7.34
  7.10
  6.89
  6.70
  6.53
  6.38
  6.24
  6.12
  6.01
  5.91
  5.82
  5.73
  5.66
  5.59
  5.53
  5.48
  5.43
Revenue, $m
  1,034
  1,181
  1,338
  1,504
  1,680
  1,866
  2,060
  2,264
  2,477
  2,699
  2,930
  3,171
  3,421
  3,681
  3,951
  4,231
  4,523
  4,826
  5,142
  5,470
  5,811
  6,167
  6,537
  6,923
  7,326
  7,746
  8,184
  8,642
  9,121
  9,621
  10,143
Variable operating expenses, $m
 
  1,053
  1,184
  1,324
  1,472
  1,627
  1,790
  1,961
  2,140
  2,326
  2,520
  2,659
  2,868
  3,086
  3,313
  3,548
  3,793
  4,047
  4,312
  4,587
  4,873
  5,171
  5,482
  5,806
  6,143
  6,495
  6,863
  7,247
  7,648
  8,067
  8,506
Fixed operating expenses, $m
 
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
Total operating expenses, $m
  938
  1,053
  1,184
  1,324
  1,472
  1,627
  1,790
  1,961
  2,140
  2,326
  2,520
  2,659
  2,868
  3,086
  3,313
  3,548
  3,793
  4,047
  4,312
  4,587
  4,873
  5,171
  5,482
  5,806
  6,143
  6,495
  6,863
  7,247
  7,648
  8,067
  8,506
Operating income, $m
  97
  128
  153
  180
  209
  239
  270
  303
  337
  373
  411
  512
  552
  594
  638
  683
  730
  779
  830
  883
  938
  996
  1,055
  1,118
  1,183
  1,251
  1,321
  1,395
  1,472
  1,553
  1,638
EBITDA, $m
  137
  198
  224
  252
  281
  312
  345
  379
  415
  452
  491
  531
  573
  616
  662
  709
  757
  808
  861
  916
  973
  1,033
  1,095
  1,159
  1,227
  1,297
  1,370
  1,447
  1,527
  1,611
  1,698
Interest expense (income), $m
  4
  5
  7
  9
  11
  14
  17
  19
  22
  25
  28
  32
  35
  39
  42
  46
  50
  54
  59
  63
  68
  73
  78
  83
  89
  94
  100
  107
  113
  120
  127
Earnings before tax, $m
  93
  123
  147
  171
  197
  225
  254
  284
  315
  348
  382
  480
  517
  556
  595
  637
  680
  725
  771
  820
  870
  923
  978
  1,035
  1,094
  1,156
  1,221
  1,289
  1,359
  1,433
  1,511
Tax expense, $m
  35
  33
  40
  46
  53
  61
  68
  77
  85
  94
  103
  130
  140
  150
  161
  172
  184
  196
  208
  221
  235
  249
  264
  279
  295
  312
  330
  348
  367
  387
  408
Net income, $m
  58
  90
  107
  125
  144
  164
  185
  207
  230
  254
  279
  351
  377
  406
  435
  465
  496
  529
  563
  598
  635
  674
  714
  755
  799
  844
  891
  941
  992
  1,046
  1,103

BALANCE SHEET

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Cash and short-term investments, $m
  8
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
Total assets, $m
  1,055
  1,195
  1,354
  1,522
  1,701
  1,888
  2,085
  2,292
  2,507
  2,732
  2,966
  3,209
  3,462
  3,725
  3,999
  4,283
  4,578
  4,885
  5,204
  5,536
  5,882
  6,242
  6,617
  7,007
  7,415
  7,840
  8,284
  8,747
  9,231
  9,737
  10,266
Adjusted assets (=assets-cash), $m
  1,047
  1,195
  1,354
  1,522
  1,701
  1,888
  2,085
  2,292
  2,507
  2,732
  2,966
  3,209
  3,462
  3,725
  3,999
  4,283
  4,578
  4,885
  5,204
  5,536
  5,882
  6,242
  6,617
  7,007
  7,415
  7,840
  8,284
  8,747
  9,231
  9,737
  10,266
Revenue / Adjusted assets
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
  0.988
Average production assets, $m
  115
  131
  148
  167
  187
  207
  229
  251
  275
  300
  325
  352
  380
  409
  439
  470
  502
  536
  571
  607
  645
  685
  726
  768
  813
  860
  908
  959
  1,012
  1,068
  1,126
Working capital, $m
  125
  133
  151
  170
  190
  211
  233
  256
  280
  305
  331
  358
  387
  416
  446
  478
  511
  545
  581
  618
  657
  697
  739
  782
  828
  875
  925
  977
  1,031
  1,087
  1,146
Total debt, $m
  135
  194
  258
  326
  398
  473
  552
  635
  722
  812
  906
  1,004
  1,106
  1,212
  1,321
  1,436
  1,554
  1,678
  1,806
  1,940
  2,078
  2,223
  2,374
  2,531
  2,695
  2,866
  3,044
  3,230
  3,425
  3,628
  3,841
Total liabilities, $m
  420
  480
  544
  612
  684
  759
  838
  921
  1,008
  1,098
  1,192
  1,290
  1,392
  1,498
  1,607
  1,722
  1,840
  1,964
  2,092
  2,226
  2,364
  2,509
  2,660
  2,817
  2,981
  3,152
  3,330
  3,516
  3,711
  3,914
  4,127
Total equity, $m
  634
  715
  810
  910
  1,017
  1,129
  1,247
  1,370
  1,499
  1,634
  1,773
  1,919
  2,070
  2,228
  2,391
  2,561
  2,738
  2,921
  3,112
  3,311
  3,517
  3,733
  3,957
  4,190
  4,434
  4,688
  4,954
  5,231
  5,520
  5,823
  6,139
Total liabilities and equity, $m
  1,054
  1,195
  1,354
  1,522
  1,701
  1,888
  2,085
  2,291
  2,507
  2,732
  2,965
  3,209
  3,462
  3,726
  3,998
  4,283
  4,578
  4,885
  5,204
  5,537
  5,881
  6,242
  6,617
  7,007
  7,415
  7,840
  8,284
  8,747
  9,231
  9,737
  10,266
Debt-to-equity ratio
  0.213
  0.270
  0.320
  0.360
  0.390
  0.420
  0.440
  0.460
  0.480
  0.500
  0.510
  0.520
  0.530
  0.540
  0.550
  0.560
  0.570
  0.570
  0.580
  0.590
  0.590
  0.600
  0.600
  0.600
  0.610
  0.610
  0.610
  0.620
  0.620
  0.620
  0.630
Adjusted equity ratio
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598
  0.598

CASH FLOW

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Net income, $m
  58
  90
  107
  125
  144
  164
  185
  207
  230
  254
  279
  351
  377
  406
  435
  465
  496
  529
  563
  598
  635
  674
  714
  755
  799
  844
  891
  941
  992
  1,046
  1,103
Depreciation, amort., depletion, $m
  40
  70
  71
  72
  73
  74
  75
  76
  77
  79
  80
  19
  21
  22
  24
  25
  27
  29
  31
  33
  35
  37
  39
  42
  44
  46
  49
  52
  55
  58
  61
Funds from operations, $m
  102
  160
  178
  197
  217
  238
  260
  283
  307
  333
  359
  370
  398
  428
  458
  490
  524
  558
  594
  631
  670
  711
  753
  797
  843
  891
  940
  993
  1,047
  1,104
  1,164
Change in working capital, $m
  -8
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  31
  32
  33
  34
  36
  37
  39
  40
  42
  44
  45
  47
  50
  52
  54
  56
  59
Cash from operations, $m
  110
  142
  160
  178
  197
  217
  238
  260
  283
  308
  333
  342
  370
  398
  428
  459
  491
  524
  558
  594
  632
  670
  711
  753
  797
  843
  891
  941
  993
  1,048
  1,105
Maintenance CAPEX, $m
  0
  -6
  -7
  -8
  -9
  -10
  -11
  -12
  -14
  -15
  -16
  -18
  -19
  -21
  -22
  -24
  -25
  -27
  -29
  -31
  -33
  -35
  -37
  -39
  -42
  -44
  -46
  -49
  -52
  -55
  -58
New CAPEX, $m
  -29
  -17
  -17
  -18
  -20
  -21
  -22
  -23
  -24
  -25
  -26
  -27
  -28
  -29
  -30
  -31
  -32
  -34
  -35
  -36
  -38
  -39
  -41
  -43
  -45
  -47
  -49
  -51
  -53
  -55
  -58
Cash from investing activities, $m
  -52
  -23
  -24
  -26
  -29
  -31
  -33
  -35
  -38
  -40
  -42
  -45
  -47
  -50
  -52
  -55
  -57
  -61
  -64
  -67
  -71
  -74
  -78
  -82
  -87
  -91
  -95
  -100
  -105
  -110
  -116
Free cash flow, $m
  58
  119
  135
  151
  168
  186
  205
  225
  246
  268
  291
  298
  323
  349
  376
  404
  433
  463
  494
  527
  561
  596
  633
  671
  711
  752
  796
  841
  888
  937
  989
Issuance/(repayment) of debt, $m
  -34
  59
  64
  68
  72
  75
  79
  83
  87
  90
  94
  98
  102
  106
  110
  114
  119
  123
  128
  133
  139
  145
  151
  157
  164
  171
  178
  186
  195
  203
  213
Issuance/(repurchase) of shares, $m
  -21
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
Cash from financing (excl. dividends), $m  
  -59
  59
  64
  68
  72
  75
  79
  83
  87
  90
  94
  98
  102
  106
  110
  114
  119
  123
  128
  133
  139
  145
  151
  157
  164
  171
  178
  186
  195
  203
  213
Total cash flow (excl. dividends), $m
  -1
  178
  199
  219
  240
  262
  284
  308
  333
  358
  385
  396
  425
  455
  486
  518
  551
  586
  623
  660
  700
  741
  784
  828
  875
  923
  974
  1,027
  1,083
  1,141
  1,201
Retained Cash Flow (-), $m
  -40
  -89
  -95
  -101
  -107
  -112
  -118
  -123
  -129
  -134
  -140
  -146
  -151
  -157
  -163
  -170
  -177
  -184
  -191
  -199
  -207
  -215
  -224
  -234
  -244
  -254
  -265
  -277
  -290
  -303
  -316
Prev. year cash balance distribution, $m
 
  8
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
Cash flow adjustment, $m
 
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
  0
Cash available for distribution, $m
 
  98
  104
  118
  133
  149
  167
  185
  204
  224
  245
  250
  273
  297
  322
  348
  375
  403
  432
  462
  493
  526
  559
  595
  631
  669
  709
  750
  793
  838
  885
Discount rate, %
 
  4.30
  4.52
  4.74
  4.98
  5.23
  5.49
  5.76
  6.05
  6.35
  6.67
  7.00
  7.35
  7.72
  8.11
  8.51
  8.94
  9.39
  9.86
  10.35
  10.87
  11.41
  11.98
  12.58
  13.21
  13.87
  14.56
  15.29
  16.05
  16.86
  17.70
PV of cash for distribution, $m
 
  94
  95
  103
  110
  116
  121
  125
  127
  129
  129
  119
  117
  113
  108
  102
  95
  88
  80
  71
  63
  54
  46
  39
  32
  26
  21
  16
  12
  9
  7
Current shareholders' claim on cash, %
  100
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0
  100.0

Navigant Consulting, Inc. provides professional services to corporate executives and senior management, corporate counsel, law firms, corporate boards, special committees, and governmental agencies worldwide. The company operates through four segments: Healthcare; Energy; Financial Services Advisory and Compliance; and Disputes, Forensics & Legal Technology. The Healthcare segment provides consulting and business process management services to healthcare providers, payers, and life sciences companies. This segment helps clients respond to market legislative changes, such as the shift to an outcome and value-based reimbursements model, ongoing industry consolidation and reorganization, Medicaid expansion, and the implementation of a new electronic health records system. The Energy segment offers advisory services to utilities, governmental agencies, manufacturers, and investors. This segment provides its clients with advisory solutions in business strategy and planning, distributed energy resources and renewables, energy efficiency and demand response, and grid modernization, as well as various benchmarking and research services. The Financial Services Advisory and Compliance segment provides strategic, operational, valuation, risk management, investigative, and compliance advisory services to clients primarily in the financial services industry, including major financial and insurance institutions. This segment also offers anti-corruption solutions and anti-money laundering, litigation support, and tax compliance and valuation services. The Disputes, Forensics & Legal Technology segment offers professional services, including accounting, regulatory, construction, and computer forensic services, as well as valuation and economic analysis. Navigant Consulting, Inc. was founded in 1983 and is headquartered in Chicago, Illinois.

FINANCIAL RATIOS  of  Navigant Consulting (NCI)

Valuation Ratios
P/E Ratio 18.7
Price to Sales 1.1
Price to Book 1.7
Price to Tangible Book
Price to Cash Flow 9.9
Price to Free Cash Flow 13.4
Growth Rates
Sales Growth Rate 12.5%
Sales - 3 Yr. Growth Rate %
EPS Growth Rate %
EPS - 3 Yr. Growth Rate %
Capital Spending Gr. Rate -27.5%
Cap. Spend. - 3 Yr. Gr. Rate 10%
Financial Strength
Quick Ratio NaN
Current Ratio 0
LT Debt to Equity 21.3%
Total Debt to Equity 21.3%
Interest Coverage 24
Management Effectiveness
Return On Assets 5.8%
Ret/ On Assets - 3 Yr. Avg. 2.9%
Return On Total Capital 7.5%
Ret/ On T. Cap. - 3 Yr. Avg. 3.5%
Return On Equity 9.4%
Return On Equity - 3 Yr. Avg. 4.6%
Asset Turnover 1
Profitability Ratios
Gross Margin 29.7%
Gross Margin - 3 Yr. Avg. 29%
EBITDA Margin 13.2%
EBITDA Margin - 3 Yr. Avg. 8.6%
Operating Margin 9.3%
Oper. Margin - 3 Yr. Avg. 5.2%
Pre-Tax Margin 9%
Pre-Tax Margin - 3 Yr. Avg. 4.7%
Net Profit Margin 5.6%
Net Profit Margin - 3 Yr. Avg. 2.7%
Effective Tax Rate 37.6%
Eff/ Tax Rate - 3 Yr. Avg. 24%
Payout Ratio 0%

NCI stock valuation input parameters

Revenue. Company's revenue (or sales) is always the starting point of any cash flow forecast. In the NCI stock intrinsic value calculation we used $1034 million for the last fiscal year's total revenue generated by Navigant Consulting. The default revenue input number comes from 2016 income statement of Navigant Consulting. You may change it if you feel that it should be adjusted for some unusual circumstances that are not expected to be repeated in the future or if you already know (from interim financial statements, for example) that this year's revenue is going to be quite different.

Revenue growth rate. Forecasted future revenue growth rate is the most important input parameter for the intrinsic value calculation. Unlike other input parameters that are reasonably expected to be in line with their historic averages or their historic trends, the revenue growth rate by and large is a wild card: nobody really knows what the company's revenue will be in the future. Of course, the level of unpredictability is different for different industries (utility companies being the most predictable and, thus, less risky).
    We use three input parameters to forecast the revenue growth rate in our NCI stock valuation model: a) initial revenue growth rate of 14.2% whose default value is the revenue growth rate in the most recent quarter compared to the quarterly revenue a year ago; b) terminal revenue growth rate of 5% whose default value is chosen to be close to the average nominal (i.e. not adjusted for inflation) GDP growth rate; and c) revenue decline factor of 0.9, which stipulates that revenue growth rate in each forecasted year will be equal to the difference of the revenue growth rate in the preceding year and the terminal revenue growth rate multiplied by this revenue decline factor (with the passage of time the revenue growth rate will be approaching the terminal revenue growth rate, but not quite reaching it - though the difference could be infinitesimally small).
    At the revenue decline factor of 1, the future revenue growth rate is forecasted to be constant and equal to the initial revenue growth rate. The smaller the revenue decline factor, the faster the revenue growth rate will approach the terminal revenue growth.

Discount rate. The discount rate is used for determining the present value of future cash flows: future cash flows are "discounted" as at normal conditions (that translate into positive expected return on investment) one dollar today is worth more than the same dollar in the future. Unlike all other valuation models, we use variable discount rate, i.e. it increases for each consecutive year. This is done to account for higher risk of cash flows coming in further in the future.
    The initial discount rate of 4.3%, whose default value for NCI is calculated based on our internal credit rating of Navigant Consulting, is applied to the cash flow expected to be received a year from now (well, actually, to be precise, in the financial year following the base year - the last year for which we have financial statements). For each consecutive year the discount rate is multiplied by the discount rate multiplier of 1.05, e.i. each year it increases by 5%. Feel free to change this number to correspond to your level of risk assessment of Navigant Consulting.
    By the way, it is easy to set the discount rate to be constant (this would make comparison with other valuation models easier): just set the discount rate multiplier equal to 1 and chose the magnitude of the initial discount rate to your liking.

Variable cost ratio is the ratio of variable costs (i.e. costs that fluctuate with fluctuation of the volume of production) to the revenue expressed as a percentage. In the calculation of intrinsic value of NCI stock the variable cost ratio is equal to 89.9%.

Fixed operating expenses is just that - expenses that are not dependant on the volume of production. They are set to $0 million in the base year in the intrinsic value calculation for NCI stock. These expenses increase with the level of inflation in subsequent years.

Interest rate on debt is the average all-in rate of interest paid by the company on its debt. It is set at 3.5% for Navigant Consulting.

Corporate tax rate of 27% is the nominal tax rate for Navigant Consulting. In reality, companies find ways to pay much less taxes than that or not to pay them at all.

Cash flow adjustment could be used for any adjustment the investor deems necessary. Most commonly we use this field to account for stock options-related effects in excess of what is reported on the company's income statement. The cash flow adjustment is expressed as a percentage of the revenue, and in the current valuation of the NCI stock is equal to 0%.

Production assets are the company's assets used for manufacturing products or provision of services. In the valuation model input table they are expressed as a percentage of revenue and for NCI are equal to 11.1%.

Life of production assets of 18.5 years is the average useful life of capital assets used in Navigant Consulting operations. It is used to calculate yearly capital expenditures needed to keep these assets in good order - we call it the maintenance CAPEX.

Working capital is the difference between the company's current assets and liabilities. In the model we use the ratio of working capital to revenue, which for NCI is equal to 11.3%. A negative number means that the company is apt at using financial resources of its suppliers and customers; a large positive number, on the other hand, means that it either provides in-kind financing to others or is not good at managing its inventories.

Book value of equity - $634 million for Navigant Consulting - is used in calculation of the "floor" for intrinsic valuation based on the discounted cash flow (DCF) method. Even if the prospects are very bad for a company, its assets could always be sold now for their current fair market value.

Shares outstanding of 47.244 million for Navigant Consulting is needed to calculate the intrinsic value of one share.

Market capitalization is used here only for reference purposes and as a quick check that the share price and the number of shares outstanding numbers are correct - something especially to be cognizant about at stock splits. So, the market capitalization of Navigant Consulting at the current share price and the inputted number of shares is $1.1 billion.


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COMPANY NEWS

▶ NCI seeks to recover $19M from alleged embezzler, CEO says in earnings call   [Apr-10-17 01:55PM  American City Business Journals]
▶ James Mapes to Lead Navigant Cymetrix   [Mar-08-17 08:30AM  Business Wire]
▶ Navigant Announces Managing Director Promotions   [Dec-21-16 09:30AM  Business Wire]
▶ With Self-Driving Cars, We're All Cartographers   [Dec-19-16 01:13PM  at Forbes]
▶ Is Navigant Consulting, Inc. (NCI) Worthy of Your Portfolio?   [Dec-15-16 09:56AM  at Insider Monkey]
▶ US Wind Generation Sets New Records Throughout 2016   [Dec-08-16 04:55PM  at Forbes]
▶ The Apple Car Was Always A Longshot   [Oct-19-16 09:15AM  at Forbes]
▶ Ford Sets A Date For Its Autonomous Vehicle Future   [Aug-19-16 02:15PM  at Forbes]
Stock chart of NCI Financial statements of NCI
Valuation of Stocks

The paper VALUATION OF STOCKS: The Quest for Intrinsic Value provides a detailed description of our valuation model and discloses the calculation algorithm.

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