Intrinsic value of Under Armour Cl C - UA

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$19.65

  Intrinsic Value

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  Value-price divergence*

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

We calculate the intrinsic value of UA 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 8.7

 

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, %
  21.75
  11.40
  10.76
  10.18
  9.67
  9.20
  8.78
  8.40
  8.06
  7.75
  7.48
  7.23
  7.01
  6.81
  6.63
  6.46
  6.32
  6.19
  6.07
  5.96
  5.86
  5.78
  5.70
  5.63
  5.57
  5.51
  5.46
  5.41
  5.37
  5.33
  5.30
Revenue, $m
  4,825
  5,375
  5,953
  6,560
  7,194
  7,855
  8,545
  9,263
  10,010
  10,786
  11,593
  12,431
  13,302
  14,208
  15,149
  16,129
  17,148
  18,208
  19,313
  20,464
  21,664
  22,916
  24,222
  25,586
  27,011
  28,499
  30,055
  31,682
  33,384
  35,165
  37,029
Variable operating expenses, $m
 
  4,815
  5,327
  5,864
  6,425
  7,011
  7,621
  8,257
  8,918
  9,605
  10,320
  11,005
  11,777
  12,578
  13,412
  14,279
  15,181
  16,120
  17,098
  18,117
  19,180
  20,288
  21,444
  22,652
  23,913
  25,231
  26,608
  28,048
  29,555
  31,132
  32,782
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
  4,408
  4,815
  5,327
  5,864
  6,425
  7,011
  7,621
  8,257
  8,918
  9,605
  10,320
  11,005
  11,777
  12,578
  13,412
  14,279
  15,181
  16,120
  17,098
  18,117
  19,180
  20,288
  21,444
  22,652
  23,913
  25,231
  26,608
  28,048
  29,555
  31,132
  32,782
Operating income, $m
  417
  560
  626
  696
  769
  845
  924
  1,006
  1,092
  1,181
  1,273
  1,426
  1,526
  1,629
  1,737
  1,850
  1,967
  2,088
  2,215
  2,347
  2,485
  2,628
  2,778
  2,934
  3,098
  3,269
  3,447
  3,634
  3,829
  4,033
  4,247
EBITDA, $m
  562
  707
  784
  863
  947
  1,034
  1,125
  1,219
  1,317
  1,420
  1,526
  1,636
  1,751
  1,870
  1,994
  2,123
  2,257
  2,396
  2,542
  2,693
  2,851
  3,016
  3,188
  3,367
  3,555
  3,751
  3,956
  4,170
  4,394
  4,628
  4,874
Interest expense (income), $m
  21
  28
  34
  41
  48
  55
  62
  70
  79
  87
  96
  105
  115
  125
  135
  146
  158
  169
  181
  194
  207
  221
  236
  251
  266
  283
  300
  318
  336
  356
  376
Earnings before tax, $m
  388
  532
  592
  655
  721
  790
  861
  936
  1,013
  1,093
  1,177
  1,320
  1,411
  1,504
  1,602
  1,704
  1,809
  1,919
  2,034
  2,153
  2,277
  2,407
  2,543
  2,684
  2,832
  2,986
  3,147
  3,316
  3,492
  3,677
  3,871
Tax expense, $m
  131
  144
  160
  177
  195
  213
  233
  253
  274
  295
  318
  356
  381
  406
  433
  460
  488
  518
  549
  581
  615
  650
  686
  725
  765
  806
  850
  895
  943
  993
  1,045
Net income, $m
  257
  389
  433
  478
  526
  576
  629
  683
  739
  798
  859
  964
  1,030
  1,098
  1,169
  1,244
  1,321
  1,401
  1,485
  1,572
  1,662
  1,757
  1,856
  1,959
  2,067
  2,180
  2,298
  2,421
  2,550
  2,684
  2,825

BALANCE SHEET

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Cash and short-term investments, $m
  250
  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
  3,644
  3,780
  4,187
  4,613
  5,059
  5,524
  6,009
  6,514
  7,039
  7,585
  8,152
  8,742
  9,355
  9,991
  10,654
  11,342
  12,059
  12,805
  13,582
  14,391
  15,235
  16,115
  17,034
  17,993
  18,995
  20,042
  21,136
  22,280
  23,477
  24,729
  26,040
Adjusted assets (=assets-cash), $m
  3,394
  3,780
  4,187
  4,613
  5,059
  5,524
  6,009
  6,514
  7,039
  7,585
  8,152
  8,742
  9,355
  9,991
  10,654
  11,342
  12,059
  12,805
  13,582
  14,391
  15,235
  16,115
  17,034
  17,993
  18,995
  20,042
  21,136
  22,280
  23,477
  24,729
  26,040
Revenue / Adjusted assets
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
  1.422
Average production assets, $m
  742
  828
  917
  1,010
  1,108
  1,210
  1,316
  1,427
  1,541
  1,661
  1,785
  1,914
  2,049
  2,188
  2,333
  2,484
  2,641
  2,804
  2,974
  3,151
  3,336
  3,529
  3,730
  3,940
  4,160
  4,389
  4,628
  4,879
  5,141
  5,415
  5,703
Working capital, $m
  1,279
  1,177
  1,304
  1,437
  1,575
  1,720
  1,871
  2,029
  2,192
  2,362
  2,539
  2,722
  2,913
  3,112
  3,318
  3,532
  3,755
  3,988
  4,230
  4,482
  4,745
  5,019
  5,305
  5,603
  5,915
  6,241
  6,582
  6,938
  7,311
  7,701
  8,109
Total debt, $m
  817
  969
  1,159
  1,358
  1,566
  1,784
  2,010
  2,246
  2,491
  2,746
  3,011
  3,286
  3,573
  3,870
  4,179
  4,501
  4,835
  5,184
  5,547
  5,925
  6,319
  6,730
  7,159
  7,607
  8,075
  8,563
  9,074
  9,609
  10,168
  10,753
  11,365
Total liabilities, $m
  1,613
  1,765
  1,955
  2,154
  2,362
  2,580
  2,806
  3,042
  3,287
  3,542
  3,807
  4,082
  4,369
  4,666
  4,975
  5,297
  5,631
  5,980
  6,343
  6,721
  7,115
  7,526
  7,955
  8,403
  8,871
  9,359
  9,870
  10,405
  10,964
  11,549
  12,161
Total equity, $m
  2,031
  2,015
  2,231
  2,459
  2,696
  2,944
  3,203
  3,472
  3,752
  4,043
  4,345
  4,659
  4,986
  5,325
  5,678
  6,045
  6,427
  6,825
  7,239
  7,670
  8,120
  8,590
  9,079
  9,590
  10,124
  10,682
  11,265
  11,875
  12,513
  13,181
  13,879
Total liabilities and equity, $m
  3,644
  3,780
  4,186
  4,613
  5,058
  5,524
  6,009
  6,514
  7,039
  7,585
  8,152
  8,741
  9,355
  9,991
  10,653
  11,342
  12,058
  12,805
  13,582
  14,391
  15,235
  16,116
  17,034
  17,993
  18,995
  20,041
  21,135
  22,280
  23,477
  24,730
  26,040
Debt-to-equity ratio
  0.402
  0.480
  0.520
  0.550
  0.580
  0.610
  0.630
  0.650
  0.660
  0.680
  0.690
  0.710
  0.720
  0.730
  0.740
  0.740
  0.750
  0.760
  0.770
  0.770
  0.780
  0.780
  0.790
  0.790
  0.800
  0.800
  0.810
  0.810
  0.810
  0.820
  0.820
Adjusted equity ratio
  0.525
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533
  0.533

CASH FLOW

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Net income, $m
  257
  389
  433
  478
  526
  576
  629
  683
  739
  798
  859
  964
  1,030
  1,098
  1,169
  1,244
  1,321
  1,401
  1,485
  1,572
  1,662
  1,757
  1,856
  1,959
  2,067
  2,180
  2,298
  2,421
  2,550
  2,684
  2,825
Depreciation, amort., depletion, $m
  145
  147
  157
  167
  178
  189
  201
  213
  226
  239
  253
  210
  225
  240
  256
  273
  290
  308
  327
  346
  367
  388
  410
  433
  457
  482
  509
  536
  565
  595
  627
Funds from operations, $m
  119
  536
  590
  646
  705
  766
  830
  896
  965
  1,037
  1,112
  1,174
  1,255
  1,339
  1,426
  1,517
  1,611
  1,709
  1,811
  1,918
  2,029
  2,145
  2,266
  2,392
  2,524
  2,662
  2,806
  2,957
  3,114
  3,279
  3,452
Change in working capital, $m
  -185
  120
  127
  133
  139
  145
  151
  157
  164
  170
  177
  184
  191
  198
  206
  214
  223
  232
  242
  252
  263
  274
  286
  299
  312
  326
  341
  356
  373
  390
  408
Cash from operations, $m
  304
  542
  463
  513
  566
  621
  679
  739
  802
  867
  935
  991
  1,064
  1,140
  1,220
  1,302
  1,388
  1,477
  1,569
  1,666
  1,766
  1,871
  1,980
  2,094
  2,212
  2,336
  2,465
  2,601
  2,742
  2,889
  3,044
Maintenance CAPEX, $m
  0
  -81
  -91
  -101
  -111
  -122
  -133
  -145
  -157
  -169
  -183
  -196
  -210
  -225
  -240
  -256
  -273
  -290
  -308
  -327
  -346
  -367
  -388
  -410
  -433
  -457
  -482
  -509
  -536
  -565
  -595
New CAPEX, $m
  -388
  -86
  -89
  -93
  -98
  -102
  -106
  -111
  -115
  -120
  -124
  -129
  -134
  -139
  -145
  -151
  -157
  -163
  -170
  -177
  -185
  -193
  -201
  -210
  -219
  -229
  -240
  -251
  -262
  -274
  -287
Cash from investing activities, $m
  -381
  -167
  -180
  -194
  -209
  -224
  -239
  -256
  -272
  -289
  -307
  -325
  -344
  -364
  -385
  -407
  -430
  -453
  -478
  -504
  -531
  -560
  -589
  -620
  -652
  -686
  -722
  -760
  -798
  -839
  -882
Free cash flow, $m
  -77
  374
  283
  319
  357
  397
  440
  484
  530
  578
  628
  665
  720
  776
  834
  895
  958
  1,023
  1,091
  1,162
  1,235
  1,311
  1,391
  1,474
  1,560
  1,650
  1,743
  1,841
  1,943
  2,050
  2,162
Issuance/(repayment) of debt, $m
  157
  179
  190
  199
  208
  217
  226
  236
  245
  255
  265
  275
  286
  297
  309
  322
  335
  348
  363
  378
  394
  411
  429
  448
  468
  489
  511
  534
  559
  585
  612
Issuance/(repurchase) of shares, $m
  15
  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  
  209
  179
  190
  199
  208
  217
  226
  236
  245
  255
  265
  275
  286
  297
  309
  322
  335
  348
  363
  378
  394
  411
  429
  448
  468
  489
  511
  534
  559
  585
  612
Total cash flow (excl. dividends), $m
  124
  554
  473
  518
  565
  615
  666
  720
  775
  833
  893
  941
  1,006
  1,073
  1,143
  1,216
  1,292
  1,372
  1,454
  1,540
  1,629
  1,723
  1,820
  1,922
  2,028
  2,139
  2,254
  2,376
  2,502
  2,635
  2,774
Retained Cash Flow (-), $m
  -363
  -207
  -217
  -227
  -238
  -248
  -258
  -269
  -280
  -291
  -302
  -314
  -327
  -339
  -353
  -367
  -382
  -398
  -414
  -431
  -450
  -469
  -490
  -511
  -534
  -558
  -583
  -610
  -638
  -668
  -699
Prev. year cash balance distribution, $m
 
  223
  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
 
  570
  256
  291
  328
  367
  408
  450
  495
  542
  591
  626
  679
  734
  791
  849
  911
  974
  1,040
  1,108
  1,179
  1,253
  1,330
  1,410
  1,494
  1,581
  1,671
  1,766
  1,864
  1,968
  2,075
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
 
  546
  234
  253
  270
  284
  296
  304
  310
  311
  310
  297
  290
  279
  265
  249
  231
  212
  191
  171
  150
  130
  110
  92
  76
  61
  49
  38
  29
  21
  16
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

Under Armour, Inc., together with its subsidiaries, develops, markets, and distributes branded performance apparel, footwear, and accessories for men, women, and youth primarily in North America, Europe, the Middle East, Africa, the Asia-Pacific, and Latin America. The company offers its apparel in compression, fitted, and loose types to be worn in hot, cold, and in between the extremes. It also provides various footwear products, including running, basketball, cleated, slides and performance training, and outdoor footwear. In addition, the company offers accessories, which include headwear, bags, and gloves; and digital fitness platform licenses and subscriptions, as well as digital advertising. Under Armour, Inc. primarily provides its products under the UA Logo, UNDER ARMOUR, UA, ARMOUR, HEATGEAR, COLDGEAR, ALLSEASONGEAR, PROTECT THIS HOUSE, and I WILL, as well as ARMOURBITE, ARMOURSTORM, ARMOUR FLEECE, ARMOUR BRA, UA RECORD, UA HEALTHBOX, and UNDER ARMOUR CONNECTED FITNESS brands. The company sells its products through wholesale channels, including national and regional sporting goods chains, independent and specialty retailers, department store chains, institutional athletic departments, and leagues and teams, as well as independent distributors; and directly to consumers through a network of brand and factory house stores, and Website. Under Armour, Inc. was founded in 1996 and is headquartered in Baltimore, Maryland.

FINANCIAL RATIOS  of  Under Armour Cl C (UA)

Valuation Ratios
P/E Ratio 33.5
Price to Sales 1.8
Price to Book 4.2
Price to Tangible Book
Price to Cash Flow 28.3
Price to Free Cash Flow -102.6
Growth Rates
Sales Growth Rate 21.8%
Sales - 3 Yr. Growth Rate %
EPS Growth Rate %
EPS - 3 Yr. Growth Rate %
Capital Spending Gr. Rate 28.9%
Cap. Spend. - 3 Yr. Gr. Rate 34.5%
Financial Strength
Quick Ratio 9
Current Ratio 0
LT Debt to Equity 38.9%
Total Debt to Equity 40.2%
Interest Coverage 19
Management Effectiveness
Return On Assets 8.3%
Ret/ On Assets - 3 Yr. Avg. 9.8%
Return On Total Capital 9.9%
Ret/ On T. Cap. - 3 Yr. Avg. 12.1%
Return On Equity 13.9%
Return On Equity - 3 Yr. Avg. 15.5%
Asset Turnover 1.5
Profitability Ratios
Gross Margin 46.4%
Gross Margin - 3 Yr. Avg. 47.9%
EBITDA Margin 11.5%
EBITDA Margin - 3 Yr. Avg. 12.5%
Operating Margin 8.6%
Oper. Margin - 3 Yr. Avg. 10.1%
Pre-Tax Margin 8%
Pre-Tax Margin - 3 Yr. Avg. 9.6%
Net Profit Margin 5.3%
Net Profit Margin - 3 Yr. Avg. 6%
Effective Tax Rate 33.8%
Eff/ Tax Rate - 3 Yr. Avg. 37.6%
Payout Ratio 1.2%

UA stock valuation input parameters

Revenue. Company's revenue (or sales) is always the starting point of any cash flow forecast. In the UA stock intrinsic value calculation we used $4825 million for the last fiscal year's total revenue generated by Under Armour Cl C. The default revenue input number comes from 2016 income statement of Under Armour Cl C. 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 UA stock valuation model: a) initial revenue growth rate of 11.4% 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 UA is calculated based on our internal credit rating of Under Armour Cl C, 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 Under Armour Cl C.
    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 UA stock the variable cost ratio is equal to 89.7%.

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 UA 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 Under Armour Cl C.

Corporate tax rate of 27% is the nominal tax rate for Under Armour Cl C. 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 UA 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 UA are equal to 15.4%.

Life of production assets of 9.1 years is the average useful life of capital assets used in Under Armour Cl C 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 UA is equal to 21.9%. 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 - $2031 million for Under Armour Cl C - 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 445.102 million for Under Armour Cl C 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 Under Armour Cl C at the current share price and the inputted number of shares is $8.7 billion.


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Stock chart of UA Financial statements of UA Annual reports of UA
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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