Intrinsic value of Titan International - TWI

Previous Close

$9.70

  Intrinsic Value

$1.25

stock screener

  Rating & Target

str. sell

-87%

Previous close

$9.70

 
Intrinsic value

$1.25

 
Up/down potential

-87%

 
Rating

str. sell

We calculate the intrinsic value of TWI 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 0.6

 

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, %
  -9.25
  10.30
  9.77
  9.29
  8.86
  8.48
  8.13
  7.82
  7.53
  7.28
  7.05
  6.85
  6.66
  6.50
  6.35
  6.21
  6.09
  5.98
  5.88
  5.80
  5.72
  5.64
  5.58
  5.52
  5.47
  5.42
  5.38
  5.34
  5.31
  5.28
  5.25
Revenue, $m
  1,266
  1,396
  1,533
  1,675
  1,824
  1,978
  2,139
  2,306
  2,480
  2,661
  2,848
  3,044
  3,246
  3,457
  3,677
  3,905
  4,143
  4,391
  4,649
  4,919
  5,200
  5,493
  5,800
  6,120
  6,455
  6,805
  7,171
  7,554
  7,955
  8,375
  8,814
Variable operating expenses, $m
 
  1,420
  1,559
  1,704
  1,855
  2,012
  2,176
  2,346
  2,522
  2,706
  2,897
  3,095
  3,302
  3,516
  3,739
  3,971
  4,213
  4,465
  4,728
  5,002
  5,288
  5,587
  5,898
  6,224
  6,564
  6,920
  7,293
  7,682
  8,090
  8,517
  8,964
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
  1,287
  1,420
  1,559
  1,704
  1,855
  2,012
  2,176
  2,346
  2,522
  2,706
  2,897
  3,095
  3,302
  3,516
  3,739
  3,971
  4,213
  4,465
  4,728
  5,002
  5,288
  5,587
  5,898
  6,224
  6,564
  6,920
  7,293
  7,682
  8,090
  8,517
  8,964
Operating income, $m
  -21
  -24
  -26
  -28
  -31
  -34
  -36
  -39
  -42
  -45
  -48
  -52
  -55
  -59
  -63
  -66
  -70
  -75
  -79
  -84
  -88
  -93
  -99
  -104
  -110
  -116
  -122
  -128
  -135
  -142
  -150
EBITDA, $m
  39
  42
  46
  51
  55
  60
  65
  70
  75
  81
  86
  92
  98
  105
  111
  118
  125
  133
  141
  149
  157
  166
  176
  185
  195
  206
  217
  229
  241
  254
  267
Interest expense (income), $m
  34
  27
  33
  40
  46
  53
  60
  68
  75
  83
  92
  100
  109
  119
  128
  139
  149
  160
  172
  183
  196
  209
  222
  237
  251
  267
  283
  300
  317
  336
  355
Earnings before tax, $m
  -33
  -51
  -59
  -68
  -77
  -87
  -97
  -107
  -118
  -129
  -140
  -152
  -165
  -178
  -191
  -205
  -220
  -235
  -251
  -267
  -284
  -302
  -321
  -341
  -361
  -382
  -405
  -428
  -453
  -478
  -505
Tax expense, $m
  3
  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
Net income, $m
  -34
  -51
  -59
  -68
  -77
  -87
  -97
  -107
  -118
  -129
  -140
  -152
  -165
  -178
  -191
  -205
  -220
  -235
  -251
  -267
  -284
  -302
  -321
  -341
  -361
  -382
  -405
  -428
  -453
  -478
  -505

BALANCE SHEET

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Cash and short-term investments, $m
  198
  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
  1,266
  1,178
  1,294
  1,414
  1,539
  1,670
  1,805
  1,946
  2,093
  2,245
  2,404
  2,568
  2,740
  2,918
  3,103
  3,295
  3,496
  3,705
  3,923
  4,151
  4,388
  4,636
  4,894
  5,165
  5,447
  5,742
  6,051
  6,375
  6,713
  7,067
  7,438
Adjusted assets (=assets-cash), $m
  1,068
  1,178
  1,294
  1,414
  1,539
  1,670
  1,805
  1,946
  2,093
  2,245
  2,404
  2,568
  2,740
  2,918
  3,103
  3,295
  3,496
  3,705
  3,923
  4,151
  4,388
  4,636
  4,894
  5,165
  5,447
  5,742
  6,051
  6,375
  6,713
  7,067
  7,438
Revenue / Adjusted assets
  1.185
  1.185
  1.185
  1.185
  1.185
  1.184
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
  1.185
Average production assets, $m
  461
  508
  558
  610
  664
  720
  779
  840
  903
  969
  1,037
  1,108
  1,182
  1,258
  1,338
  1,421
  1,508
  1,598
  1,692
  1,790
  1,893
  2,000
  2,111
  2,228
  2,350
  2,477
  2,610
  2,750
  2,896
  3,048
  3,208
Working capital, $m
  363
  289
  317
  347
  378
  410
  443
  477
  513
  551
  590
  630
  672
  716
  761
  808
  858
  909
  962
  1,018
  1,076
  1,137
  1,201
  1,267
  1,336
  1,409
  1,484
  1,564
  1,647
  1,734
  1,825
Total debt, $m
  506
  499
  593
  691
  793
  899
  1,010
  1,125
  1,245
  1,369
  1,498
  1,633
  1,772
  1,918
  2,069
  2,226
  2,390
  2,561
  2,738
  2,924
  3,118
  3,320
  3,531
  3,751
  3,982
  4,223
  4,475
  4,739
  5,015
  5,304
  5,607
Total liabilities, $m
  969
  962
  1,056
  1,154
  1,256
  1,362
  1,473
  1,588
  1,708
  1,832
  1,961
  2,096
  2,235
  2,381
  2,532
  2,689
  2,853
  3,024
  3,201
  3,387
  3,581
  3,783
  3,994
  4,214
  4,445
  4,686
  4,938
  5,202
  5,478
  5,767
  6,070
Total equity, $m
  297
  217
  238
  260
  283
  307
  332
  358
  385
  413
  442
  473
  504
  537
  571
  606
  643
  682
  722
  764
  807
  853
  901
  950
  1,002
  1,057
  1,113
  1,173
  1,235
  1,300
  1,369
Total liabilities and equity, $m
  1,266
  1,179
  1,294
  1,414
  1,539
  1,669
  1,805
  1,946
  2,093
  2,245
  2,403
  2,569
  2,739
  2,918
  3,103
  3,295
  3,496
  3,706
  3,923
  4,151
  4,388
  4,636
  4,895
  5,164
  5,447
  5,743
  6,051
  6,375
  6,713
  7,067
  7,439
Debt-to-equity ratio
  1.704
  2.300
  2.490
  2.650
  2.800
  2.930
  3.040
  3.140
  3.230
  3.310
  3.390
  3.460
  3.520
  3.570
  3.620
  3.670
  3.720
  3.760
  3.790
  3.830
  3.860
  3.890
  3.920
  3.950
  3.970
  4.000
  4.020
  4.040
  4.060
  4.080
  4.100
Adjusted equity ratio
  0.093
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184
  0.184

CASH FLOW

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Net income, $m
  -34
  -51
  -59
  -68
  -77
  -87
  -97
  -107
  -118
  -129
  -140
  -152
  -165
  -178
  -191
  -205
  -220
  -235
  -251
  -267
  -284
  -302
  -321
  -341
  -361
  -382
  -405
  -428
  -453
  -478
  -505
Depreciation, amort., depletion, $m
  60
  66
  72
  79
  86
  94
  101
  109
  117
  126
  135
  144
  153
  163
  174
  185
  196
  208
  220
  233
  246
  260
  274
  289
  305
  322
  339
  357
  376
  396
  417
Funds from operations, $m
  52
  15
  13
  11
  9
  7
  5
  2
  0
  -3
  -6
  -8
  -11
  -14
  -17
  -20
  -24
  -27
  -31
  -35
  -38
  -43
  -47
  -51
  -56
  -61
  -66
  -71
  -77
  -82
  -89
Change in working capital, $m
  8
  27
  28
  29
  31
  32
  33
  35
  36
  37
  39
  40
  42
  44
  45
  47
  49
  51
  53
  56
  58
  61
  63
  66
  69
  72
  76
  79
  83
  87
  91
Cash from operations, $m
  44
  -12
  -15
  -18
  -22
  -25
  -29
  -32
  -36
  -40
  -44
  -49
  -53
  -58
  -63
  -68
  -73
  -79
  -84
  -90
  -97
  -103
  -110
  -118
  -125
  -133
  -142
  -150
  -160
  -169
  -180
Maintenance CAPEX, $m
  0
  -60
  -66
  -72
  -79
  -86
  -94
  -101
  -109
  -117
  -126
  -135
  -144
  -153
  -163
  -174
  -185
  -196
  -208
  -220
  -233
  -246
  -260
  -274
  -289
  -305
  -322
  -339
  -357
  -376
  -396
New CAPEX, $m
  -42
  -48
  -50
  -52
  -54
  -56
  -59
  -61
  -63
  -66
  -68
  -71
  -74
  -77
  -80
  -83
  -87
  -90
  -94
  -98
  -102
  -107
  -112
  -117
  -122
  -127
  -133
  -139
  -146
  -153
  -160
Cash from investing activities, $m
  -90
  -108
  -116
  -124
  -133
  -142
  -153
  -162
  -172
  -183
  -194
  -206
  -218
  -230
  -243
  -257
  -272
  -286
  -302
  -318
  -335
  -353
  -372
  -391
  -411
  -432
  -455
  -478
  -503
  -529
  -556
Free cash flow, $m
  -46
  -120
  -131
  -143
  -155
  -168
  -181
  -194
  -209
  -223
  -238
  -254
  -271
  -288
  -306
  -325
  -344
  -365
  -386
  -408
  -432
  -456
  -482
  -508
  -536
  -566
  -597
  -629
  -663
  -698
  -735
Issuance/(repayment) of debt, $m
  -5
  90
  94
  98
  102
  106
  111
  115
  120
  124
  129
  134
  140
  145
  151
  157
  164
  171
  178
  186
  194
  202
  211
  221
  231
  241
  252
  264
  276
  289
  303
Issuance/(repurchase) of shares, $m
  0
  72
  81
  90
  100
  111
  122
  133
  145
  157
  169
  182
  196
  210
  225
  240
  257
  273
  291
  309
  328
  348
  369
  390
  413
  437
  462
  488
  515
  544
  573
Cash from financing (excl. dividends), $m  
  -5
  162
  175
  188
  202
  217
  233
  248
  265
  281
  298
  316
  336
  355
  376
  397
  421
  444
  469
  495
  522
  550
  580
  611
  644
  678
  714
  752
  791
  833
  876
Total cash flow (excl. dividends), $m
  -51
  42
  44
  46
  48
  49
  51
  54
  56
  58
  60
  62
  65
  68
  70
  73
  76
  79
  83
  86
  90
  94
  98
  103
  107
  112
  117
  123
  128
  134
  141
Retained Cash Flow (-), $m
  48
  -72
  -81
  -90
  -100
  -111
  -122
  -133
  -145
  -157
  -169
  -182
  -196
  -210
  -225
  -240
  -257
  -273
  -291
  -309
  -328
  -348
  -369
  -390
  -413
  -437
  -462
  -488
  -515
  -544
  -573
Prev. year cash balance distribution, $m
 
  101
  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
 
  71
  -37
  -45
  -53
  -61
  -70
  -79
  -89
  -99
  -109
  -120
  -131
  -143
  -155
  -167
  -180
  -194
  -208
  -223
  -238
  -254
  -270
  -288
  -306
  -325
  -344
  -365
  -387
  -409
  -433
Discount rate, %
 
  7.70
  8.09
  8.49
  8.91
  9.36
  9.83
  10.32
  10.83
  11.38
  11.95
  12.54
  13.17
  13.83
  14.52
  15.25
  16.01
  16.81
  17.65
  18.53
  19.46
  20.43
  21.45
  22.52
  23.65
  24.83
  26.07
  27.38
  28.75
  30.18
  31.69
PV of cash for distribution, $m
 
  66
  -32
  -35
  -38
  -39
  -40
  -40
  -39
  -37
  -35
  -33
  -30
  -27
  -23
  -20
  -17
  -14
  -11
  -9
  -7
  -5
  -4
  -3
  -2
  -1
  -1
  -1
  0
  0
  0
Current shareholders' claim on cash, %
  100
  84.1
  70.7
  59.1
  49.4
  41.1
  34.2
  28.4
  23.5
  19.4
  16.1
  13.2
  10.9
  9.0
  7.4
  6.1
  5.0
  4.1
  3.4
  2.8
  2.3
  1.9
  1.5
  1.2
  1.0
  0.8
  0.7
  0.6
  0.5
  0.4
  0.3

Titan International, Inc. is a wheel, tire, and undercarriage industrial manufacturer and supplier. The Company's segments are agricultural, earthmoving/construction, and consumer. The Company produces a range of products to meet the specifications of original equipment manufacturers (OEMs) and aftermarket customers in the agricultural, earthmoving/construction, and consumer markets. Its agricultural products include rims, wheels, tires, and undercarriage systems and components manufactured for use on various agricultural equipment. Its earthmoving/construction products include rims, wheels, tires, and undercarriage systems and components for various types of off-the-road (OTR) earthmoving, mining, military, construction, and forestry equipment. The Company's consumer products include, but are not limited to, bias truck tires in Latin America and light truck tires in Russia, as well as products for all-terrain vehicles (ATVs), turf, and golf cart applications.

FINANCIAL RATIOS  of  Titan International (TWI)

Valuation Ratios
P/E Ratio -15.5
Price to Sales 0.4
Price to Book 1.8
Price to Tangible Book
Price to Cash Flow 11.9
Price to Free Cash Flow 262.7
Growth Rates
Sales Growth Rate -9.2%
Sales - 3 Yr. Growth Rate %
EPS Growth Rate %
EPS - 3 Yr. Growth Rate %
Capital Spending Gr. Rate -12.5%
Cap. Spend. - 3 Yr. Gr. Rate -12.1%
Financial Strength
Quick Ratio 2
Current Ratio 0
LT Debt to Equity 137.7%
Total Debt to Equity 170.4%
Interest Coverage 0
Management Effectiveness
Return On Assets 0.2%
Ret/ On Assets - 3 Yr. Avg. -1.4%
Return On Total Capital -4.1%
Ret/ On T. Cap. - 3 Yr. Avg. -6.4%
Return On Equity -10.6%
Return On Equity - 3 Yr. Avg. -13.9%
Asset Turnover 1
Profitability Ratios
Gross Margin 11.2%
Gross Margin - 3 Yr. Avg. 10.2%
EBITDA Margin 4.8%
EBITDA Margin - 3 Yr. Avg. 2.3%
Operating Margin -1.7%
Oper. Margin - 3 Yr. Avg. -2.8%
Pre-Tax Margin -2.6%
Pre-Tax Margin - 3 Yr. Avg. -4.8%
Net Profit Margin -2.7%
Net Profit Margin - 3 Yr. Avg. -4.1%
Effective Tax Rate -9.1%
Eff/ Tax Rate - 3 Yr. Avg. -22.6%
Payout Ratio -2.9%

TWI stock valuation input parameters

Revenue. Company's revenue (or sales) is always the starting point of any cash flow forecast. In the TWI stock intrinsic value calculation we used $1266 million for the last fiscal year's total revenue generated by Titan International. The default revenue input number comes from 2016 income statement of Titan International. 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 TWI stock valuation model: a) initial revenue growth rate of 10.3% 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 7.7%, whose default value for TWI is calculated based on our internal credit rating of Titan International, 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 Titan International.
    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 TWI stock the variable cost ratio is equal to 101.7%.

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 TWI 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 6.7% for Titan International.

Corporate tax rate of 27% is the nominal tax rate for Titan International. 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 TWI 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 TWI are equal to 36.4%.

Life of production assets of 7.7 years is the average useful life of capital assets used in Titan International 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 TWI is equal to 20.7%. 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 - $297 million for Titan International - 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 59.658 million for Titan International 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 Titan International at the current share price and the inputted number of shares is $0.6 billion.

RELATED COMPANIES Price Int.Val. Rating
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COMPANY NEWS

▶ Titan International Inc's Recovery Hits a Snag   [Aug-03-17 02:34PM  Motley Fool]
▶ Titan International reports 2Q loss   [06:20AM  Associated Press]
▶ Titan International reports 1Q loss   [06:10AM  Associated Press]
▶ 3 Industrial Stocks Struggling in March   [Mar-31-17 11:04AM  Motley Fool]
▶ Titan International reports 4Q loss   [06:14AM  Associated Press]
▶ Titan International, Inc. Announces CFO Appointment   [Dec-06-16 09:11PM  PR Newswire]
▶ The Best Dividend Stocks of 2016   [Nov-17-16 12:30PM  at Motley Fool]
▶ 2 Top Rubber Stocks to Buy Today   [Nov-09-16 08:22AM  at Motley Fool]
▶ Titan International Prepping For Demand Recovery in 2017   [Nov-04-16 08:36PM  at Motley Fool]
▶ 3 Stocks That Have Doubled in 2016   [Oct-25-16 05:59AM  at Motley Fool]
▶ Why Titan International Inc's Shares Surged 39% in August   [Sep-09-16 05:24PM  at Motley Fool]
Financial statements of TWI
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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