Financial modeling: [uses Excel]
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass. [u.a.]
MIT Press
2014
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIV, 1111 S. Ill., graph. Darst. |
| ISBN: | 9780262027281 |
Internformat
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| 245 | 1 | 0 | |a Financial modeling |b [uses Excel] |c Simon Benninga |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 2014 | |
| 300 | |a XXIV, 1111 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Finance Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804151877435129856 |
|---|---|
| adam_text | Titel: Financial modeling
Autor: Benninga, Simon
Jahr: 2014
Contents
Preface xxi
Before All Else 1
0.1 Data Tables 1
0.2 What Is Getformula? 1
0.3 How to Put Getformula into Your Excel Notebook 1
0.4 Saving the Excel Workbook: Windows 4
0.5 Saving the Excel Workbook: Mac 5
0.6 Do You Have to Put Getformula into Each Excel Workbook? 6
0.7 A Shortcut to Use Getformula 6
0.8 Recording Getformula: The Windows Case 7
0.9 Recording Getformula: The Mac Case 10
CORPORATE FINANCE AND VALUATION 11
Basic Financial Calculations 13
1.1 Overview 13
1.2 Present Value and Net Present Value 14
1.3 The Internal Rate of Return (IRR) and Loan Tables 20
1.4 Multiple Internal Rates of Return 27
1.5 Fiat Payment Schedules 29
1.6 Future Values and Applications 30
1.7 A Pension Problem-Complicating the Future Value Problem 33
1.8 Continuous Compounding 38
1.9 Discounting Using Dated Cash Flows 42
Exercises 45
Corporate Valuation Overview 53
2.1 Overview 53
2.2 Four Methods to Compute Enterprise Value (EV) 53
2.3 Using Accounting Book Values to Value a Company.
The Firm s Accounting Enterprise Value 54
2.4 The Efficient Markets Approach to Corporate Valuation 58
2.5 Enterprise Value (EV) as the Present Value of the Free
Cash Flows: DCF Top Down Valuation 60
Contents
2.6 Free Cash Flows Based on Consolidated Statement of
Cash Flows (CSCF) 63
2.7 ABC Corp., Consolidated Statement of Cash Flows (CSCF) 64
2.8 Free Cash Flows Based on Pro Forma Financial Statements 67
2.9 Summary 69
Exercises 70
Calculating the Weighted Average Cost of Capital (WACC) 71
3.1 Overview 71
3.2 Computing the Value of the Firm s Equity, E 73
3.3 Computing the Value of the Firm s Debt, D 74
3.4 Computing the Firm s Tax Rate, Tc 75
3.5 Computing the Firm s Cost of Debt, rD 76
3.6 Two Approaches to Computing the Firm s Cost of Equity, rE 82
3.7 Implementing the Gordon Model for rE 82
3.8 The CAPM: Computing the Beta, ß 89
3.9 Using the Security Market Line (SML) to Calculate Merck s
Cost of Equity, rE 96
3.10 Three Approaches to Computing the Expected Return on the
Market, E(rM) 98
3.11 What s the Risk-Free Rate rf in the CAPM? 102
3.12 Computing the WACC, Three Cases 102
3.13 Computing the WACC for Merck (MRK) 103
3.14 Computing the WACC for Whole Foods (WFM) 104
3.15 Computing the WACC for Caterpillar (CAT) 106
3.16 When Don t the Models Work? 109
3.17 Summary 113
Exercises 113
Valuation Based on the Consolidated Statement of Cash Flows 117
4.1 Overview 117
4.2 Free Cash Flow (FCF): Measuring the Cash Produced
by the Business 119
4.3 A Simple Example 121
4.4 Merck: Reverse Engineering the Market Value 124
4.5 Summary 126
Exercise 126
Contents
Pro Forma Financial Statement Modeling 127
5.1 Overview 127
5.2 How Financial Models Work: Theory and an Initial Example 127
5.3 Free Cash Flow (FCF): Measuring the Cash Produced
by the Business 136
5.4 Using the Free Cash Flow (FCF) to Value the Firm and Its
Equity 138
5.5 Some Notes on the Valuation Procedure 140
5.6 Alternative Modeling of Fixed Assets 142
5.7 Sensitivity Analysis 144
5.8 Debt as a Plug 145
5.9 Incorporating a Target Debt/Equity Ratio into a Pro Forma 148
5.10 Project Finance: Debt Repayment Schedules 150
5.11 Calculating the Return on Equity 153
5.12 Tax Loss Carryforwards 155
5.13 Summary 157
Exercises 157
Building a Pro Forma Model: The Case of Caterpillar 161
6.1 Overview 161
6.2 Caterpillar s Financial Statements, 2007-2011 162
6.3 Analyzing the Financial Statements 166
6.4 A Model for Caterpillar 176
6.5 Using the Model to Value Caterpillar 177
6.6 Summary 178
Financial Analysis of Leasing 179
7.1 Overview 179
7.2 A Simple but Misleading Example 179
7.3 Leasing and Firm Financing-The Equivalent-Loan Method 181
7.4 The Lessor s Problem: Calculating the Highest Acceptable
Lease Rental 184
7.5 Asset Residual Value and Other Considerations 187
7.6 Leveraged Leasing 189
7.7 A Leveraged Lease Example 190
7.8 Summary 193
Exercises 193
Contents
II PORTFOLIO MODELS 195
8 Portfolio Models-Introduction 197
8.1 Overview 197
8.2 Computing Returns for Apple (AAPL) and Google (GOOG) 197
8.3 Calculating Portfolio Means and Variances 202
8.4 Portfolio Mean and Variance-Case of N Assets 205
8.5 Envelope Portfolios 210
8.6 Summary 213
Exercises 213
Appendix 8.1: Adjusting for Dividends 215
Appendix 8.2: Continuously Compounded Versus Geometrie
Returns 218
9 Calculating Efficient Portfolios 221
9.1 Overview 221
9.2 Some Preliminary Definitions and Notation 221
9.3 Five Propositions on Efficient Portfolios and the CAPM 223
9.4 Calculating the Efficient Frontier: An Example 227
9.5 Finding Efficient Portfolios in One Step 234
9.6 Three Notes on the Optimization Procedure 236
9.7 Finding the Market Portfolio: The Capital Market Line (CML) 239
9.8 Testing the SML-Implementing Propositions 3-5 242
9.9 Summary 245
Exercises 246
Mathematical Appendix 248
10 Calculating the Variance-Covariance Matrix 251
10.1 Overview 251
10.2 Computing the Sample Variance-Covariance Matrix 251
10.3 The Correlation Matrix 256
10.4 Computing the Global Minimum Variance Portfolio (GMVP) 259
10.5 Four Alternatives to the Sample Variance-Covariance Matrix 261
10.6 Alternatives to the Sample Variance-Covariance:
The Single-Index Model (SIM) 262
10.7 Alternatives to the Sample Variance-Covariance:
Constant Correlation 264
Contents
10.8 Alternatives to the Sample Variance-Covariance:
Shrinkage Methods 266
10.9 Using Option Information to Compute the Variance Matrix 268
10.10 Which Method to Compute the Variance-Covariance Matrix? 271
10.11 Summary 272
Exercises 272
11 Estimating Betas and the Security Market Line 273
11.1 Overview 273
11.2 Testing the SML 276
11.3 Did We Learn Something? 280
11.4 The Non-Efficiency of the Market Portfolio 283
11.5 So What s the Real Market Portfolio? How Can We Test
the CAPM? 285
11.6 Using Excess Returns 286
11.7 Summary: Does the CAPM Have Any Uses? 288
Exercises 288
12 Efficient Portfolios Without Short Sales 291
12.1 Overview 291
12.2 A Numerical Example 292
12.3 The Efficient Frontier with Short-Sale Restrictions 298
12.4 A VBA Program for the Efficient Frontier Without Short
Sales 299
12.5 Other Position Restrictions 302
12.6 Summary 303
Exercise 303
13 The Black-Litterman Approach to Portfolio Optimization 305
13.1 Overview 305
13.2 A Naive Problem 307
13.3 Black and Litterman s Solution to the Optimization Problem 313
13.4 BL Step 1: What Does the Market Think? 313
13.5 BL Step 2: Introducing Opinions-What Does Joanna
Think? 316
13.6 Using Black-Litterman for International Asset Allocation 324
13.7 Summary 328
Exercises 329
Contents
14 Event Studies 331
14.1 Overview 331
14.2 Outline of an Event Study 331
14.3 An Initial Event Study: Procter Gamble Buys Gillette 335
14.4 A Füller Event Study: Impact of Earnings Announcements
on Stock Prices 342
14.5 Using a Two-Factor Model of Returns for an Event Study 350
14.6 Using Excel s Offset Function to Locate a Regression
in a Data Set 355
14.7 Summary 357
III VALUATION OF OPTIONS 359
15 Introduction to Options 361
15.1 Overview 361
15.2 Basic Option Definitions and Terminology 361
15.3 Some Examples 364
15.4 Option Payoff and Profit Patterns 365
15.5 Option Strategies: Payoffs from Portfolios of Options and
Stocks 370
15.6 Option Arbitrage Propositions 372
15.7 Summary 379
Exercises 380
16 The Binomial Option Pricing Model 383
16.1 Overview 383
16.2 Two-Date Binomial Pricing 383
16.3 State Prices 385
16.4 The Multi-Period Binomial Model 389
16.5 Pricing American Options Using the Binomial Pricing Model 395
16.6 Programming the Binomial Option Pricing Model in VBA 398
16.7 Convergence of Binomial Pricing to the Black-Scholes Price 404
16.8 Using the Binomial Model to Price Employee Stock Options 408
16.9 Using the Binomial Model to Price Non-Standard Options:
An Example 417
16.10 Summary 419
Exercises 419
xiii Contents
17 The Black-Scholes Model 425
17.1 Overview 425
17.2 The Black-Scholes Model 425
17.3 Using VBA to Define a Black-Scholes Pricing Function 427
17.4 Calculating the Volatility 430
17.5 A VBA Function to Find the Implied Volatility 434
17.6 Dividend Adjustments to the Black-Scholes 437
17.7 Using the Black-Scholes Formula to Price Structured
Securities 441
17.8 Bang for the Bück with Options 457
17.9 The Black (1976) Model for Bond Option Valuation 459
17.10 Summary 462
Exercises 462
18 Option Greeks 467
18.1 Overview 467
18.2 Defining and Computing the Greeks 468
18.3 Delta Hedging a Call 474
18.4 Hedging a Collar 476
18.5 Summary 485
Exercises 486
Appendix: VBA for Greeks 486
19 Real Options 493
19.1 Overview 493
19.2 A Simple Example of the Option to Expand 494
19.3 The Abandonment Option 497
19.4 Valuing the Abandonment Option as a Series of Puts 503
19.5 Valuing a Biotechnology Project 505
19.6 Summary 511
Exercises 512
TV VALUING BONDS 515
20 Duration 517
20.1 Overview 517
20.2 Two Examples 517
xiv Contents
20.3 What Does Duration Mean? 520
20.4 Duration Patterns 524
20.5 The Duration of a Bond with Uneven Payments 525
20.6 Non-Flat Term Structures and Duration 533
20.7 Summary 536
Exercises 536
21 Immunization Strategies 539
21.1 Overview 539
21.2 A Basic Simple Model of Immunization 539
21.3 A Numerical Example 541
21.4 Convexity: A Continuation of Our Immunization
Experiment 545
21.5 Building a Better Mousetrap 547
21.6 Summary 551
Exercises 551
22 Modeling the Term Structure 553
22.1 Overview 553
22.2 Basic Example 553
22.3 Several Bonds with the Same Maturity 558
22.4 Fitting a Functional Form to the Term Structure 562
22.5 The Properties of the Nelson-Siegel Term Structure 566
22.6 Term Structure for Treasury Notes 569
22.7 An Additional Computational Improvement 571
22.8 Nelson-Siegel-Svensson Model 573
22.9 Summary 574
Appendix: VBA Functions Used in This Chapter 575
23 Calculating Default-Adjusted Expected Bond Returns 579
23.1 Overview 579
23.2 Calculating the Expected Return in a One-Period Framework 581
23.3 Calculating the Bond Expected Return in a Multi-Period
Framework 582
23.4 A Numerical Example 587
23.5 Experimenting with the Example 589
23.6 Computing the Bond Expected Return for an Actual Bond 591
Contents
23.7 Semiannual Transition Matrices 596
23.8 Computing Bond Beta 599
23.9 Summary 602
Exercises 603
V MONTE CARLO METHODS 605
24 Generating and Using Random Numbers 607
24.1 Overview 607
24.2 Rand( ) and Rnd: The Excel and VBA Random-Number
Generators 608
24.3 Testing Random-Number Generators 611
24.4 Generating Normally Distributed Random Numbers 617
24.5 Norm.Inv: Another Way to Generate Normal Deviates 628
24.6 Generating Correlated Random Numbers 630
24.7 What s Our Interest in Correlation? A Small Case 635
24.8 Multiple Random Variables with Correlation:
The Cholesky Decomposition 638
24.9 Multivariate Normal with Non-Zero Means 646
24.10 Multivariate Uniform Simulations 648
24.11 Summary 651
Exercises 651
25 An Introduction to Monte Carlo Methods 655
25.1 Overview 655
25.2 Computing n Using Monte Carlo 655
25.3 Writing a VBA Program 661
25.4 Another Monte Carlo Problem: Investment and Retirement 663
25.5 A Monte Carlo Simulation of the Investment Problem 667
25.6 Summary 671
Exercises 671
26 Simulating Stock Prices 675
26.1 Overview 675
26.2 What Do Stock Prices Look Like? 676
26.3 Lognormal Price Distributions and Geometrie Diffusions 681
26.4 What Does the Lognormal Distribution Look Like? 684
xvi Contents
26.5 Simulating Lognormal Price Paths 688
26.6 Technical Analysis 692
26.7 Calculating the Parameters of the Lognormal Distribution
from Stock Prices 694
26.8 Summary 696
Exercises 696
27 Monte Carlo Simulations for Investments 699
27.1 Overview 699
27.2 Simulating Price and Returns for a Single Stock 699
27.3 Portfolio of Two Stocks 702
27.4 Adding a Risk-Free Asset 706
27.5 Multiple Stock Portfolios 708
27.6 Simulating Savings for Pensions 710
27.7 Beta and Return 715
27.8 Summary 720
Exercises 720
28 Value at Risk (VaR) 723
28.1 Overview 723
28.2 A Really Simple Example 723
28.3 Defining Quantiles in Excel 725
28.4 A Three-Asset Problem: The Importance of the
Variance-Covariance Matrix 728
28.5 Simulating Data: Bootstrapping 730
Appendix: How to Bootstrap: Making a Bingo Card in Excel 736
29 Simulating Options and Option Strategies 745
29.1 Overview 745
29.2 Imperfect but Cashless Replication of a Call Option 747
29.3 Simulating Portfolio Insurance 750
29.4 Some Properties of Portfolio Insurance 758
29.5 Digression: Insuring Total Portfolio Returns 759
29.6 Simulating a Butterfly 765
29.7 Summary 771
Exercises 772
xvii Contents
30 Using Monte Carlo Methods for Option Pricing 775
30.1 Overview 775
30.2 Pricing a Plain-Vanilla Call Using Monte Carlo Methods 776
30.3 State Prices, Probabilities, and Risk Neutrality 780
30.4 Pricing a Call Using the Binomial Monte Carlo Model 782
30.5 Monte Carlo Plain-Vanilla Call Pricing Converges to
Black-Scholes 786
30.6 Pricing Asian Options 794
30.7 Pricing Asian Options with a VBA Program 802
30.8 Pricing Barrier Options with Monte Carlo 807
30.9 Using VBA and Monte Carlo to Price a Barrier Option 811
30.10 Summary 817
Exercises 817
VI EXCEL TECHNIQUES 821
31 Data Tables 823
31.1 Overview 823
31.2 An Example 823
31.3 Setting Up a One-Dimensional Data Table 824
31.4 Building a Two-Dimensional Data Table 826
31.5 An Aesthetic Note: Hiding the Formula Cells 827
31.6 Excel Data Tables Are Arrays 828
31.7 Data Tables on Blank Cells (Advanced) 829
31.8 Data Tables Can Stop Your Computer 835
Exercises 836
32 Matrices 839
32.1 Overview 839
32.2 Matrix Operations 840
32.3 Matrix Inverses 843
32.4 Solving Systems of Simultaneous Linear Equations 845
32.5 Some Homemade Matrix Functions 846
Exercises 851
xviii Contents
33 Excel Functions 855
33.1 Overview 855
33.2 Financial Functions 855
33.3 Dates and Date Functions 863
33.4 The Functions XIRR, XNPV 869
33.5 Statistical Functions 875
33.6 Regressions with Excel 879
33.7 Conditional Functions 889
33.8 Large and Rank, Percentile, and PercentRank 890
33.9 Count, CountA, Countlf, Countlfs, Averagelf, Averagelfs 891
33.10 Boolean Functions 894
33.11 Offset 896
34 Array Functions 899
34.1 Overview 899
34.2 Some Built-In Excel Array Functions 899
34.3 Homemade Array Functions 904
34.4 Array Formulas with Matrices 907
Exercises 911
35 Some Excel Hints 913
35.1 Overview 913
35.2 Fast Copy: Filling in Data Next to Filled-In Column 913
35.3 Filling Cells with a Series 915
35.4 Multi-Line Cells 916
35.5 Multi-Line Cells with Text Formulas 917
35.6 Writing on Multiple Spreadsheets 918
35.7 Moving Multiple Sheets of an Excel Notebook 919
35.8 Text Functions in Excel 920
35.9 Chart Titles That Update 920
35.10 Putting Greek Symbols in Cells 924
35.11 Superscripts and Subscripts 925
35.12 Named Cells 926
35.13 Hiding Cells (in Data Tables and Other Places) 928
35.14 Formula Auditing 930
35.15 Formatting Millions as Thousands 932
35.16 Excel s Personal Notebook: Automating Frequent Procedures 934
xix Contents
VII VISUAL BASIC FOR APPLICATIONS (VBA) 943
36 User-Defined Functions with VBA 945
36.1 Overview 945
36.2 Using the VBA Editor to Build a User-Defined Function 945
36.3 Providing Help for User-Defined Functions in the Function
Wizard 955
36.4 Saving Excel Workbook with VBA Content 958
36.5 Fixing Mistakes in VBA 960
36.6 Conditional Execution: Using If Statements in VBA
Functions 963
36.7 The Boolean and Comparison Operators 967
36.8 Loops 970
36.9 Using Excel Functions in VBA 977
36.10 Using User-Defined Functions in User-Defined Functions 979
Exercises 981
Appendix: Cell Errors in Excel and VBA 986
37 Variables and Arrays 989
37.1 Overview 989
37.2 Defining Function Variables 989
37.3 Arrays and Excel Ranges 992
37.4 Simple VBA Arrays 995
37.5 Multidimensional Arrays 1005
37.6 Dynamic Arrays and the ReDim Statement 1007
37.7 Array Assignment 1009
37.8 Variants Containing an Array 1011
37.9 Arrays as Parameters to Functions 1012
37.10 Using Types 1015
37.11 Summary 1016
Exercises 1017
38 Subroutines and User Interaction 1023
38.1 Overview 1023
38.2 Subroutines 1023
38.3 User Interaction 1030
38.4 Using Subroutines to Change the Excel Workbook 1033
xx Contents
38.5 Modules 1036
38.6 Summary 1040
Exercises 1040
39 Objects and Add-Ins 1047
39.1 Overview 1047
39.2 Introduction to Worksheet Objects 1047
39.3 The Range Object 1049
39.4 The With Statement 1053
39.5 Collections 1055
39.6 Names 1061
39.7 Add-Ins and Integration 1064
39.8 Summary 1068
Exercises 1068
Selected References 1073
Index 1085
|
| any_adam_object | 1 |
| author | Benninga, Simon 1947-2015 |
| author_GND | (DE-588)170013359 |
| author_facet | Benninga, Simon 1947-2015 |
| author_role | aut |
| author_sort | Benninga, Simon 1947-2015 |
| author_variant | s b sb |
| building | Verbundindex |
| bvnumber | BV041649829 |
| classification_rvk | QP 700 QP 730 QP 890 |
| classification_tum | WIR 681f |
| ctrlnum | (OCoLC)880752284 (DE-599)GBV766498050 |
| dewey-full | 332.015118 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.015118 |
| dewey-search | 332.015118 |
| dewey-sort | 3332.015118 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV041649829 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:01:48Z |
| institution | BVB |
| isbn | 9780262027281 |
| language | English |
| lccn | 2013032409 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027090469 |
| oclc_num | 880752284 |
| open_access_boolean | |
| owner | DE-634 DE-11 DE-898 DE-BY-UBR DE-2070s DE-1049 DE-20 DE-945 DE-473 DE-BY-UBG DE-706 DE-91 DE-BY-TUM DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-634 DE-11 DE-898 DE-BY-UBR DE-2070s DE-1049 DE-20 DE-945 DE-473 DE-BY-UBG DE-706 DE-91 DE-BY-TUM DE-92 DE-355 DE-BY-UBR |
| physical | XXIV, 1111 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | MIT Press |
| record_format | marc |
| spelling | Benninga, Simon 1947-2015 Verfasser (DE-588)170013359 aut Financial modeling [uses Excel] Simon Benninga 4. ed. Cambridge, Mass. [u.a.] MIT Press 2014 XXIV, 1111 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Finance Mathematical models Finanzierung (DE-588)4017182-6 gnd rswk-swf CD-ROM (DE-588)4139307-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Microsoft Visual Basic for applications Finanzierung (DE-588)4017182-6 s Mathematisches Modell (DE-588)4114528-8 s CD-ROM (DE-588)4139307-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027090469&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Benninga, Simon 1947-2015 Financial modeling [uses Excel] Finance Mathematical models Finanzierung (DE-588)4017182-6 gnd CD-ROM (DE-588)4139307-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4017182-6 (DE-588)4139307-7 (DE-588)4114528-8 |
| title | Financial modeling [uses Excel] |
| title_auth | Financial modeling [uses Excel] |
| title_exact_search | Financial modeling [uses Excel] |
| title_full | Financial modeling [uses Excel] Simon Benninga |
| title_fullStr | Financial modeling [uses Excel] Simon Benninga |
| title_full_unstemmed | Financial modeling [uses Excel] Simon Benninga |
| title_short | Financial modeling |
| title_sort | financial modeling uses excel |
| title_sub | [uses Excel] |
| topic | Finance Mathematical models Finanzierung (DE-588)4017182-6 gnd CD-ROM (DE-588)4139307-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Finance Mathematical models Finanzierung CD-ROM Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027090469&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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