time value of money

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The Investopedia Guide to Wall Speak: The Terms You Need to Know to Talk Like Cramer, Think Like Soros, and Buy Like Buffett by Jack (edited By) Guinan

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Albert Einstein, asset allocation, asset-backed security, Brownian motion, business process, capital asset pricing model, clean water, collateralized debt obligation, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, discounted cash flows, diversification, diversified portfolio, dividend-yielding stocks, equity premium, fixed income, implied volatility, index fund, interest rate swap, inventory management, London Interbank Offered Rate, margin call, market fundamentalism, mortgage debt, passive investing, performance metric, risk tolerance, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, statistical model, time value of money, transaction costs, yield curve, zero-coupon bond

Related Terms: • Capital • Mezzanine Financing • Venture Capital • Capital Structure • Private Equity Time Value of Money What Does Time Value of Money Mean? The idea that money available today is worth more than the same amount of money in the future, based on its earnings potential. This principle asserts that money can earn interest and grow, and so any amount of money is worth more the sooner a person has it so that that person can put it to use now rather than later. Also referred to as present discounted value. Investopedia explains Time Value of Money Everyone knows that money deposited in a savings account will earn interest.

Related Terms: • Capital Asset Pricing Model—CAPM • Capital Structure • Venture Capital • Capital Gain • Depreciation Capital Asset Pricing Model (CAPM) What Does Capital Asset Pricing Model (CAPM) Mean? A model that describes the relationship between risk and expected return; it is used to price securities. The general idea behind CAPM is that investors need to be compensated for investing their cash in two ways: (1) time value of money and (2) risk. (1) The time value of money is represented by the risk-free (rf) rate in the formula and compensates investors for placing money in any investment over 36 The Investopedia Guide to Wall Speak a period of time. (2) Risk calculates the amount of compensation the investor needs for taking on additional risk.

A model of price variation over time in financial instruments such as stocks that often is used to calculate the price of a European call option. The model assumes that the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model incorporates the constant price variation of the stock, the time value of money, the option’s strike price, and the time to the option’s expiration. Also known as the Black-Scholes-Merton Model. Investopedia explains Black Scholes Model The Black Scholes Model is one of the most important concepts in modern financial theory. It was developed in 1973 by Fisher Black, Robert Merton, and Myron Scholes and is used widely today and regarded as one of the best formulas for determining option prices.


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Financial Independence by John J. Vento

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Affordable Care Act / Obamacare, Albert Einstein, asset allocation, diversification, diversified portfolio, estate planning, financial independence, fixed income, high net worth, Home mortgage interest deduction, mortgage debt, mortgage tax deduction, oil shock, Own Your Own Home, passive income, risk tolerance, time value of money, transaction costs, young professional, zero day

If you have a significant estate you must meet with an experienced estate attorney and implement some of the advanced tax planning techniques mentioned in this chapter. c10.indd 284 26/02/13 2:47 PM 11 C H A P T E R The Time Value of Money O ne of the most important concepts to accumulating wealth and becoming financially independent is understanding the time value of money. By far, the most valuable asset we have is time, but unfortunately it is usually something we take for granted and then do not fully appreciate until later in life. The time value of money formulas are highly complex mathematical equations, beyond the scope of this book; however, I recommend you purchase a financial calculator, which can perform these calculations for you.

Annual Interest Rate Future Amount > $50,000 $100,000 $200,000 $400,000 $800,000 $1,600,000 1% 2084-Dec 2156-Nov 2228-Nov 2300-Oct 2372-Oct 2444-Sep 2% 2048-Dec 2084-Dec 2120-Dec 2156-Nov 2192-Nov 2228-Nov 3% 2036-Dec 2060-Dec 2084-Dec 2108-Dec 2132-Dec 2156-Nov 4% 2030-Dec 2048-Dec 2066-Dec 2084-Dec 2102-Dec 2120-Dec 5% 2027-May 2041-Oct 2056-Mar 2070-Jul 2084-Dec 2099-May (Continued ) c11.indd 287 26/02/13 11:37 AM 288 Financial Independence (Getting to Point X ) Exhibit 11.1 (Continued ) Annual Interest Rate Future Amount > $50,000 $100,000 $200,000 $400,000 $800,000 $1,600,000 2084-Dec 6% 2024-Dec 2036-Dec 2048-Dec 2060-Dec 2072-Dec 7% 2023-Apr 2033-Jul 2043-Nov 2054-Feb 2064-May 2074-Sep 8% 2021-Dec 2030-Dec 2039-Dec 2048-Dec 2057-Dec 2066-Dec 9% 2020-Dec 2028-Dec 2036-Dec 2044-Dec 2052-Dec 2060-Dec 10% 2020-Mar 2027-May 2034-Aug 2041-Oct 2048-Dec 2056-Mar 11% 2019-Jul 2026-Jan 2032-Aug 2039-Mar 2045-Sep 2052-Mar 12% 2018-Dec 2024-Dec 2030-Dec 2036-Dec 2042-Dec 2048-Dec 13% 2018-Jul 2024-Jan 2029-Aug 2035-Feb 2040-Sep 2046-Mar 14% 2018-Feb 2023-Apr 2028-Jun 2033-Jul 2038-Sep 2043-Nov 15% 2017-Oct 2022-Aug 2027-May 2032-Mar 2036-Dec 2041-Oct 16% 2017-Jul 2021-Dec 2026-Jun 2030-Dec 2035-Jun 2039-Dec 17% 2017-Mar 2021-Jun 2025-Sep 2029-Dec 2034-Mar 2038-May 18% 2016-Dec 2020-Dec 2024-Dec 2028-Dec 2032-Dec 2036-Dec 19% 2016-Oct 2020-Jul 2024-May 2028-Feb 2031-Dec 2035-Sep 20% 2016-Aug 2020-Mar 2023-Oct 2027-May 2030-Dec 2034-Aug These mathematical facts are accurate and verifiable, yet most people are astonished when they truly understand the power of compounding and how powerful the time value of money can be. In Chapter 8, Planning for Retirement, we discussed the retirement equation of how to achieve financial independence and reach point X. After having a better appreciation for the time value of money, you can now understand why it is so critical to pay close attention to these key factors. Achieving the highest rate of return within your risk tolerance (Chapter 9, Managing Your Investments) is a critical component to this equation.

Tax System 12 Organizing and Retaining Your Records 15 Tax-Preparation Services 16 Accumulating Wealth through Tax Planning 18 ix ftoc.indd ix 26/02/13 11:17 AM x Contents Chapter 3 Chapter 4 Chapter 5 Chapter 6 ftoc.indd x Determining Your Financial Position 23 Figuring Your Financial Net Worth 24 Case Study: How One Couple Learned They Were Spending More Than They Earned 24 Making Sense of Cash Flow 35 Establishing Your Financial Goals 57 Finding Trusted Advisors 61 Managing Debt 67 Case Study: How Two Doctors Went Bankrupt in Only a Few Years—What Not to Do 67 Basic Principles for Managing Debt 71 Good Debt versus Bad Debt 73 Credit-Card Debt 74 Auto Loans 80 Student Loans 81 Home Mortgage Loans 82 Business and Investment Loans 86 Understanding Credit 87 Your Credit Report and Your Credit Score 89 Preventing Identity Theft 93 Analyzing Your Debt 94 Insuring Your Health and Life 99 Choosing a Health Insurance Plan 100 Long-Term Care Insurance 111 Disability Insurance 118 Life Insurance 122 Buying Insurance Policies 128 Protecting Your Property with Insurance 133 Case Study: How a Lack of Insurance Wiped Out One Woman’s Life Savings 134 Homeowner’s Insurance 136 Automobile Insurance 140 Umbrella Liability Insurance 144 Buying Insurance Policies 147 26/02/13 11:17 AM Contents Chapter 7 Chapter 8 Chapter 9 Paying for College 153 Case Study: How Not Saving for Your Child’s Education Can Ruin Your Finances—and Your Child’s 156 Conducting a “Needs Analysis” for Your Children’s College Educations 160 Strategies for Saving Money for College Education 162 Education Tax Deductions and Credits 179 Planning for Retirement 187 Case Study: Saving versus Not Saving for Retirement: The $1.7 Million Difference 187 Retirement Equation: Calculating Your Personal Point X 191 The High Cost of Waiting to Save for Retirement 193 What You Can Expect to Receive from Social Security 196 Qualified Retirement Plans 198 The Difference between Traditional IRAs and Roth IRAs 203 Fixed and Variable Annuities 209 Retirement Funding: “Needs Analysis” 212 Managing Your Investments 221 Analyzing Your Risk Tolerance 222 Stocks, Bonds, Mutual Funds, and Exchange-Traded Funds 226 Diversification and Modern Portfolio Theory 234 Asset Allocation and Rebalancing 237 Dollar-Cost Averaging 243 Inflation and Taxes: The Biggest Drains on Investment Return 245 Medicare Surtax on Net Investment Income 246 Chapter 10 Preserving Your Estate ftoc.indd xi xi 251 The Federal Gift and Estate Tax System 252 Legal Documents to Consider for Estate Planning 252 The Probate and Administration Process and Why You May Want to Avoid It 257 Using a Planned Gifting Strategy 261 Ownership of Property and How It Is Transferred 262 Reasons for Creating a Trust 265 Benefit from a Family Limited Partnership 277 Estate Tax Planning and Life Insurance 278 26/02/13 11:17 AM xii ftoc.indd xii Contents Chapter 11 The Time Value of Money 285 The Rule of 72 286 Appendix A: Selecting a Trusted Advisor 301 Appendix B: 101 Ways to Save $20 or More per Week 311 Appendix C: Basic Concepts and Definitions of Various Types of Taxes 321 About the Author 341 Index 343 26/02/13 11:17 AM Preface Living the American Dream M y first clients were quintessential examples of successful American Dreamers.


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Money Changes Everything: How Finance Made Civilization Possible by William N. Goetzmann

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, Cass Sunstein, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, corporate governance, Credit Default Swap, David Ricardo: comparative advantage, debt deflation, delayed gratification, Detroit bankruptcy, disintermediation, diversified portfolio, double entry bookkeeping, Edmond Halley, en.wikipedia.org, equity premium, financial independence, financial innovation, financial intermediation, fixed income, frictionless, frictionless market, full employment, high net worth, income inequality, index fund, invention of the steam engine, invention of writing, invisible hand, James Watt: steam engine, joint-stock company, joint-stock limited liability company, laissez-faire capitalism, Louis Bachelier, mandelbrot fractal, market bubble, means of production, money: store of value / unit of account / medium of exchange, moral hazard, new economy, passive investing, Paul Lévy, Ponzi scheme, price stability, principal–agent problem, profit maximization, profit motive, quantitative trading / quantitative finance, random walk, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, too big to fail, trade liberalization, trade route, transatlantic slave trade, transatlantic slave trade, tulip mania, wage slave

In all likelihood, so did financiers who traded in lottery tickets, and perhaps issuers and purchasers of life annuities, for whom the time value of money figured heavily. One of de Moivre’s most important contributions is a formula for a fixed stream of future payments over a fixed number of years. In 1724, he used his valuation method in A Treatise of Annuities on Lives. He gives credit to his friend Halley’s earlier calculations, but also suggests that he is able to improve on them. De Moivre noted that the time value of money seriously complicates the calculations for correctly valuing life annuities. The age of the policyholder mattered even more than Halley supposed.

In fact, he may even have supplied bread to the capital city of Larsa, which lay a day’s travel to the north. He was also the “grain supplier to the King”—one of his tablets was a receipt from a monthly issue to Rim-Sin for more than 5,000 liters of grain.1 There is little doubt that Dumuzi-gamil’s loan represented the productive use of the time value of money. When he borrowed business capital from Shumi-abum, he apparently had a plan for increasing his wealth. Perhaps it was the entrepreneurial idea of setting up institutional bakeries. It appears likely that debt in the hands of Ur’s entrepreneurs like Dumuzi-gamil could be a means to social and economic mobility.

Courts specifically for maritime cases were held from September to April, when ships were not at sea and business could be settled in time for the next season. I argue in this chapter that the unique features of the Athenian court system created a financially literate society with a keen sense of abstractions, such as the price of risk, the time value of money, and the negotiability and hypothecation of entire business enterprises. ATHENS AND GRAIN In 386 BCE, a group of Athenian grain dealers faced the death penalty. They were on trial for price-fixing and hoarding. Their apparent crime was collusion in negotiating the price of grain with importing merchants.

Mathematics for Finance: An Introduction to Financial Engineering by Marek Capinski, Tomasz Zastawniak

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Black-Scholes formula, Brownian motion, capital asset pricing model, cellular automata, delta neutral, discounted cash flows, discrete time, diversified portfolio, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, martingale, quantitative trading / quantitative finance, random walk, short selling, stochastic process, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

Introduction: A Simple Market Model . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Basic Notions and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 No-Arbitrage Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 One-Step Binomial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Risk and Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Forward Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Call and Put Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 Managing Risk with Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2. Risk-Free Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Periodic Compounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Streams of Payments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Continuous Compounding . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 How to Compare Compounding Methods . . . . . . . . . . . . . . 2.2 Money Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Zero-Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Money Market Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 21 22 24 29 32 35 39 39 41 43 3.

It is also equivalent to borrowing money to purchase a share for $100 today and repaying $110 to clear the loan at time 1. Chapter 9 on financial engineering will discuss various ways of managing risk with options: magnifying or reducing risk, dealing with complicated risk exposure, and constructing payoff profiles tailor made to meet the specific needs of an investor. 2 Risk-Free Assets 2.1 Time Value of Money It is a fact of life that $100 to be received after one year is worth less than the same amount today. The main reason is that money due in the future or locked in a fixed term account cannot be spent right away. One would therefore expect to be compensated for postponed consumption. In addition, prices may rise in the meantime and the amount will not have the same purchasing power as it would have at present.

We shall be concerned mainly with two questions: What is the future value of an amount invested or borrowed today? What is the present value of an amount to be paid or received at a certain time in the future? The answers depend on various factors, which will be discussed in the present chapter. This topic is often referred to as the time value of money. 21 22 Mathematics for Finance 2.1.1 Simple Interest Suppose that an amount is paid into a bank account, where it is to earn interest. The future value of this investment consists of the initial deposit, called the principal and denoted by P , plus all the interest earned since the money was deposited in the account.


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Guide to business modelling by John Tennent, Graham Friend, Economist Group

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correlation coefficient, discounted cash flows, double entry bookkeeping, iterative process, purchasing power parity, RAND corporation, shareholder value, the market place, time value of money

Future cash flows, however, must be adjusted to allow them to be compared on an equivalent basis with cash flows that take place at the start of the project. Future cash flows must be adjusted for the “time value of money” and a “risk premium”. Time value of money The time value of money reflects the principal that cash received today is worth less than the same amount of cash received in a year’s time. A rational investor would prefer $100 today rather than $100 in a year’s time as the $100 today could be invested in a bank where it would earn interest and grow to an amount greater than the $100 received in a year’s time. The discount rate, used in dcf analysis, incorporates the time value of money by including the risk-free rate of return that could be earned on $100 invested risk-free at, say, a bank or in a government bond.

The problem with payback is that it is very short term. It fails to consider cash flows beyond the payback period (for example, the project could make $2,000,000 in year 6 and its payback would still be 2 years 4 months), and therefore says nothing about the scale of the project. It also ignores the time value of money, which is explained in the next section. However, it remains one of the most popular project appraisal techniques used by companies. DISCOUNTED CASH FLOW THEORY Typical projects normally involve a sequence of cash outflows followed by a sequence of cash inflows. Discounted cash flow or dcf analysis calculates the net cash flow as if all the future cash outflows and inflows occurred simultaneously at the same point in time, which is normally the first day of the project.

140–41 capital gains tax 258 cars 131 cash 198, 202 deficits 157 surpluses 154, 157 cash breakeven point 146 cash flow 13, 33, 60, 130, 130, 136, 141, 172, 189 adjusting 153 anticipated 151 cumulative project cash flow 152 and equity value 186 forecasts 70 free (FCF) 163, 173, 173, 180 net 146 operational 147, 152 projected 257 short time intervals 180 sign convention 176 statements 156, 157, 159, 161, 169 tax and 127, 174 timing 164, 176–7, 177 cash flow cycle 140, 140, 141, 141, 202, 202 causative techniques 85 cell comments 251–2 chart wizard button 53 check boxes 223–4 circular references 159, 211 COC see cost of capital coefficients 97, 100, 103 collinearity 105 colour scheme 67 column consistency 210 column widths 69 company acquisitions 146 company law 70 company valuation model 190–92 competition 4, 15, 257 compounding 182 computers crash 36, 39 purchase 131 CONCATENATE function 44–5, 50, 263–4 conceptual errors 206 conditional formatting 52–3 Consolidate box 37–8, 38 consumers credit 78 expenditure 14 spending patterns 88 consumption proportion 131 INDEX control toolbox 222 convertibles 149, 155 corporate decision-making 13 corporate planning pyramid 12–13, 12 corporation tax 163, 164, 167, 172, 174, 258 cost of capital (COC) 204, 205 costs 147, 172, 173, 257 capital 60, 117 drivers of 123–7 fixed 122–3, 122, 123 inflexible 125, 125 operating see operating costs COUNT IF function 47, 48, 48, 264 covenants 156 CPM see Critical Path Method credit agencies 151 credit controllers 123, 123 creditor days 145, 202 creditors 145, 145, 147 critical factors 15, 16, 17, 23, 29 Critical Path Method (CPM) 11 currency 14, 46, 46, 80, 168 current liabilities 147 customer segmentation 112–13, 113, 114 cyclical component 89 D data assumptions 6, 7 collection 6, 7, 8, 22–3, 24 labels 38, 54 scenarios 61 warehousing 8 data collection manager 9 data screens 240, 240, 241 DATA VALIDATION function 53 DCF analysis see discounted cash flow analysis de minimus rule 128 debentures 148 debt 147, 150, 151, 155, 157, 204 bad 160–63 doubtful 160–61 funders 155 funding 152 instruments 157, 157 net 155 debt to equity ratios 155–6, 156, 190 debtor days 142, 162, 202 debtors 142–3, 147, 160, 161 debugging see testing and debugging decision-making analysis 1 273 INDEX choice 2 corporate 13 implementation 2 defining the outputs 12–18 alignment with the business’s overall objectives 12–13 business model output checklist 18 creating an output template 16, 17 defining the outputs required to answer the question 13–14 establish the basics 14 model outputs and corporate decisionmaking 13 real versus nominal forecasts 14 specify the time frame and period length 13–14 identifying the critical factors that determine the outputs 15 running a workshop 17–18 demand 75, 107, 108 demand curve 87 downward-sloping 86, 87 demographic shifts 18 dependencies 258 dependency ranking 242–4 depreciation 33, 34, 46, 118, 128, 129, 187, 203 other depreciation methods 131 reducing balance 130, 130, 137, 137 straight line 129–30, 130, 132, 136, 136 development log 35, 38 dialog boxes 252 discount factor 191 discount rates 45, 180, 183 discounted cash flow analysis 172, 181, 185, 188 company valuation example 190–92 EBITDA exit multiples 189 growth rate models 188–9 terminal values 188 valuation range 190 discounted cash flow theory 179–82 discounted cash flows 34, 182–3 discounting 182 distribution 117, 133–4 divide by zero 51 dividend cover 204 dividends 147, 180 documenting the model documentation outside the model contents of a typical user’s guide 255 continuing user support 255 fit for the purpose 253 good document form design 253–4, 254 structure 254 training material 255 user’s documentation 254 documentation within the model 251–3 cell comments 251–2 dialog boxes 252 macro comments 252–3, 253 specific help software 252 text boxes 252 need for documentation 250 when to document 250 where to document 250–51 Du Pont 11, 199 dynamic effects 59 dynamic links the CONCATENATE function 44 multiple models 36–7 E earnings per share 204 EBITDA (earnings before interest, tax, depreciation and amortisation), multiples 187–8, 189, 190, 192, 203, 257 economic added value (EVA) 204 economy of scale 119, 120, 120, 175, 176, 200 Edit Links box 37, 37 endogenous variables 22 enterprise value (EV) 186, 188 environmental risk 249 equity 147, 150, 151, 155, 157, 204 equity value 186 Excel Scenario Manager 248 exchange rates 15, 53, 70, 150, 167, 168, 258 behaviour 80–81 definition and uses 80 modelling approach 81–3 seed 80 exit options 257 exit screens 239–40 exogenous variables 22 EXP function 264 extrapolation techniques 85 eyeball lines 55 F FIFO (first in first out) basis 139 file folder structure 36, 36 file-naming convention 35 finance calculations 34 financial performance 18 FIND 210–11 firm value 186 fixed asset turnover 201 274 fixed assets see under capital expenditure and working capital fixed costs see under operating costs fonts 67 for and next loops 234–6 FORECAST function 95, 95, 96 forecasting, revenue see revenue forecasting forecasts 13 nominal 14 real 14 foreign exchange calculations 167–70 generic approach to modelling foreign exchange gains and losses 168 modelling foreign exchange gains and losses on overseas financing 169–70, 170, 171 modelling foreign exchange gains and losses on overseas revenue and costs 169 principles of foreign exchange accounting 167–8 format painter 50–51 formatting 67–9 colours 67 column widths 69 fonts 67 lines 67, 68 macros 218–19 number styles 68 Forms toolbar 221–5 formula bar 41, 41 formulae, deconstructing complex 208–9, 209 free cash flow (FCF) 163, 173, 173, 180, 186, 191, 205 free-form development 32 FREEZE PANES command 229–30, 230 funding see modelling funding issues G Gantt chart 10, 11 GDP see gross domestic product gearing 155, 156, 190, 245 GO TO function 53 GOAL SEEK function 242–4 goal statement 18 Gordon Growth Model 189, 190, 192 graphs 53–8, 60, 261–2, 262 eyeball lines 55 fixed cost 122, 122 improving the appearance of 54 market value 129, 129 one graph suits all 55–8, 56 triangulation 126 variable costs 119, 119 INDEX gridlines 54 gross additions/connections 88, 93, 97, 97, 98, 98, 104 gross domestic product (GDP) 15, 76, 84, 189 behaviour 71–2 definition and uses 70–71 modelling approach 72–4 seed 71 group sheet function 39 growth 205, 258 GROWTH function 106 growth rate 45, 71, 72, 74, 74, 75 H hard coding 38, 60 hedging techniques 150 HELP function 51 hiding information 69 hyperlinks 226–7, 227 I IF function 45–6, 47, 51, 65, 73, 74, 77, 120, 145, 211, 223, 264 implementation 2, 6, 7, 9 income distribution 15 levels 15 INDEX function 46, 101, 103, 103, 104, 108, 264–5 inflation 14, 15, 53, 70, 75, 132, 258 inflation rate behaviour 75–6 definition and uses 75 modelling approach 76–7 seed 75 inflexible costs see under operating costs information, hiding 69 input sheets 59–65, 60, 61, 72, 72 input timelines 29, 29, 30, 31 inputs additional 29 alternative 22 analysis 23, 24 extreme 213 inflation 76, 76 seed 19 strategic 30 uncertainty/impact 23–4, 23, 25 validation 66 variables 6, 7 interest 147, 156, 180 interest calculations 157 interest costs 131 INDEX interest income and charges alternative approaches to modelling interest income 159–60, 159, 160 interest rate assumptions 158 issues in modelling interest income and charges 158 modelling interest income and circular references 158–9 interest rates 14, 15, 53 assumptions 158 base see base interest rates interface sheets 36 internal rate of return (IRR) 13, 172, 183–5, 183, 184, 245, 257 more than one 184–5, 185 investment commencement of 258 investment funding 203 net 157 overseas 150–51 reinvestment ratio 203 investment control 149 investor measures dividend cover 204 earnings per share 204 IRR see internal rate of return IRR function 265 ISDATE function 240 ISERROR function 46, 51, 211, 213, 265 ISSER function 265 J J curve 146, 146, 152, 154 joint ownership 149 judgmental techniques 85 L land residual value 132 leases 149 operating (rents) 147 LEN function 265 lending rates 152 leverage 155 lines, in formatting 67–8, 68 LINEST function 100–101, 101, 102, 103, 104, 108, 266 list box 224, 225 LN function 266 loans 149, 152, 156 losses 163, 165, 168 M macroeconomic factors 15, 70–84 275 base interest rates 78–80 exchange rates 80–83 gross domestic product 70–75 inflation rate 75–7 other macroeconomic variables 84 population 83–4 macroeconomic forecasts 8 macroeconomics 70 macros 216–21 calculation 233, 233 comments 252–3, 253 editing the macro code 218 macros for repeated tasks 218–21 creating a personalised toolbar 221 formatting macros 218–19 personal macros 218 protecting the model 219–21 Monte Carlo 245, 246 multiplication tables 234–6, 234, 235 print macro 231, 231 recording simple 216 running the macro 218 viewing macro code 216–17, 217 manual code review 208 market growth 15 market liberalisation 18 market size 15 market value 129, 129, 130, 132 mathematical operations 209–10 MAX function 45, 125, 135, 179, 196, 266 mean square error (MSE) 99 media 19 microeconomic variables 15 microeconomics 70 Microsoft Excel 2, 4, 37, 40, 50, 51, 53, 90, 106, 180, 183, 210, 216, 218, 227, 234, 235, 236, 237, 239 milestones 10, 258 MIN function 45, 139, 154, 196, 266–7 mission statement 18 mobile telecommunications industry bottom-down/top-up forecasting 88 critical factors 15, 16 decomposition of revenue 86 penetration 105, 106, 107, 109, 111, 111 product cycle life 106, 107 regression analysis 97, 106 segmentation 112 third-generation mobile data services 88 total revenue 115, 116 MOD function 50, 125, 134 model developer 9 model development process management 32–9 276 best practice in model development avoiding some common pitfalls 39 the basics of quality control 35–8 the model development process create workings pages for all main sections and develop calculations 33 develop the user interfaces and conduct user testing 34 set up output and input templates 33 test and debug 33 transfer results to output pages 33 a model development project plan 34 establishing a modelling charter 34 using material from the modeller’s library 34 populate input templates with base or test data 33 styles of development 32 free-form development 32 model layout 59–60, 59 model outputs 13, 17, 259–62 model ownership 35 modeller’s toolbox 40–58 naming sheets 40 range names 40–44 useful features conditional formatting 52–3 divide by zero 51 format painter 51–2 macros for repeated tasks 218–21 one graph suits all 55–8 shortcut keys 50–51 using graphs 53–5 useful functions AND and OR 46–7 AVERAGE 50 CONCATENATE 44–5 MIN, MAX or IF statements 45–6 MOD 50 OFFSET 49–50, 49 SUM IF and COUNT IF 47–9, 48 modelling funding issues 146–57 cost of funding 151–2 debt to equity ratios 155–6, 156 funding strips 152–4 identifying the cash flow to be funded 147 operating environment 150–51 project control 149–50 putting the funding cost back in the model 156–7 balance sheet 157 cash flow statement 157 profit and loss account 156–7, 157 INDEX time periods 154–5, 154 types of funding 147–9 weighted average cost of capital 152 modularisation 63 Monte Carlo analysis 245–8 moving average 90, 91, 92 MSE see mean square error multiplicative model 96 multiple models and dynamic links 36–7 multiple regression 85, 87, 101–4, 102, 103, 104, 105 N naming sheets 40 navigation see under spreadsheet applications NCF see net cash flow net book value 130, 138, 139, 140, 140 net cash flow (NCF) 182 net debt 155 net operating profit after tax 204 net present value (NPV) 13, 172, 179, 182, 183, 184, 184, 189, 190, 194, 242, 243, 245, 257 nominal forecasts 14 NPV see net present value NPV function 267 number styles 68–9 numbers for an output 4 negative 4 within a formula 4 O OFFSET function 49–50, 49, 57, 119, 125, 134, 135, 138, 224, 248, 267 operating costs 29, 31, 60, 117–27, 161 completeness of operating costs 117, 117–18 cost behaviour 118 drivers of costs 123–7 inflation 126–7 inflexible costs 125, 125 tax 127 triangulation 126, 126 fixed costs 122–3, 122, 123, 125, 126, 200 variable costs 118–22 operating environment 19, 149, 150–51 operating profit 186 operational risk 248, 249 options 148 OR function 46–7, 267–8 ordinary shares 148 output sheets 33, 60, 63, 63, 64, 248 output template 16, 17, 18 277 INDEX outputs 6, 7, 23, 29 presenting model 259–62 overdrafts 149 overheads, allocated 175 overseas investments 150–51 P P/E ratios 186–7, 188 packaging 117 payback 172, 177–9, 245, 257 payroll cost 126, 203 PBT see profit before tax PED see price elasticity of demand penetration 105, 106, 107–12, 109, 114, 115 total 114 period ends 14 period length 14 PERT (Performance Evaluation and Review Technique) 10–11 PEST analysis 21 plant residual value 131–2 utilisation 258 PLC see product life cycle population 70 behaviour 83 definition and uses 83 growth 15 modelling approach 83–4 seed 83 post-project review 6, 7 PPP see purchasing power parity preference shares 148 prepayments 141, 141, 142 present value 182 price elasticity of demand (PED) 86–7, 87, 115 prices constant 14 fall in 4 print ranges 231 probability models 19 product life cycle (PLC) 106, 107, 107, 189 product prices 53 profit and loss 33, 60, 164, 257 profit and loss account 129, 141, 143, 156–7, 157, 161, 162, 163, 167, 169, 173 profit before tax (PBT) 181 profit flow 172 profit margin 199–200 profits 14 operating 186 programming techniques with Visual Basic 232–6 project appraisal and company valuation 172–92 conventions for setting out the cash flows 176–7 sign convention 176 timing 176–7, 177 discounted cash flow theory 179–82 calculating the discount rate 180 calculating the WACC 181 dicounted cash flow decision rule 182 discount rate 180 risk premium 179 short time intervals 180 time value of money 179 discounting cash flows in practice 182–3 evaluating companies 185–92 techniques for valuing companies 186–8 using DCF analysis in practice to value companies 188–92 identifying the relevant project cash flows 172–6 the cash effect of change 174–5 dealing with allocated overheads 175 group versus project 176 relevant costs and capital expenditure 174 relevant revenues 174 relevant taxes 174, 174 internal rate of return 183–5, 183, 184 more than one IRR 184–5, 184 payback 177–9 project appraisal and valuation techniques 172 project control 149–50 project manager 8, 9, 10 Project Plan see under business modelling process property space requirement 123, 124, 124 utilisation of 258 protecting the model see under spreadsheet applications purchase, timing of 132 purchase cost 131 purchase tax 127 purchasing power parity (PPP) 80, 81 R R2 value 97, 98, 102 radio (option) buttons 222–3, 223 range names 4, 40–44, 158, 159, 164, 191 accessing the named inputs and rows 44 common range names 43–4 defining several individual names 42, 42 278 naming one cell 41 naming one cell where the cell name is displayed to the left of reference value 41, 41 naming several values at once 42–3, 42 naming whole rows 43 range test the model 212–13 RANK function 268 ratios 60 the Du Pont pyramid of ratios 199–203 balance sheet management 201–2 further analysis 202–3 percentage of sales measures 201 profit margin and asset turnover 199–201 external analysis 194 internal analysis 194–5 internal ratio analysis 195 interpreting 196–7 average 196 high and low values 196 rank 196 useful ratios to calculate return on average capital employed (ROACE) 198 return on equity (ROE) 199 return on net assets (RONA) 197–8, 198, 199, 200, 201, 204 real forecasts 14 recalculation 69 reducing balance 130, 130 regression equation 98, 98 regression techniques see under revenue forecasting regulatory environment 70 rents 147 replicating actual results 212 report style 259 research agencies 8, 70 residual (“disturbance”) component 89 residual value 132 retail price index 75 return on average capital employed (ROACE) 198 return on capital employed (ROCE) 242, 243, 245, 257 return on equity (ROE) 199 return on net assets (RONA) 197–8, 198, 199, 200, 201, 204 return on sales (ROS) 257 revenue 14, 30, 53, 60, 64, 117, 147, 172, 173 decomposition 86 derivation of 29 total 86, 115–16, 116 INDEX revenue forecasting 14, 85–116 approaches to bottom-up versus top-down forecasting 87–8 classification of forecasting methodologies 85 decomposition of revenue 86 price elasticity of demand 86–7, 87 time frame 88 long-term forecasting 105–11 fitting a product life cycle curve 107–11 the product life cycle 107, 107 regression techniques 96–105 estimating the coefficients 97–9, 97, 98 forecasting using the TREND function 100, 100 limitations of regression analysis 105 the LINEST function 100–101, 101 multiple regression 101–4, 102, 103, 104, 105 regression analysis 96–7 the TREND function 99, 100 segmentation 112–16 business segment 114–15, 114, 115 consumer segment 112–13, 113, 114 mix effects 116 total revenue 115–16, 116 time series analysis 85, 87, 88–96 additive and multiplicative models 89–90, 90 components of a time series 89 estimating the trend and seasonal factors manually 91–4, 92, 93, 94 estimating the trend using the built-in moving average function 90–91, 91 forecasting using the trend, seasonal factors and the additive model 94–5, 95 limitations of time series analysis 96 the multiplicative model 96 time series data 88, 89 revenue multiples 188 revenue tax 163 ripple effect 51 risk 149, 150, 151, 155 assumption 248, 249 commercial 257 environmental 249 operational 248, 249 premium 179 ROACE see return on average capital employed ROCE see return on capital employed ROE see return on equity RONA see return on net assets INDEX ROS see return on sales ROUND function 154, 268 rounding 65–6, 65, 66, 259 ROUNDOWN function 268 ROUNDUP function 123, 133, 268 row consistency 210 rows versus columns 261, 261 S sales forecast 55 tax 127, 163–4 saving the model regularly 36 scenario development 25–31 scenario planning benefits 20 the development of 20 stage 1: identifying high impact, highly uncertain inputs 20, 21–4 stage 2: identify alternative development paths for key inputs 20, 25–6, 25–6 stage 3: select the three or four most informative scenarios 20, 26–8, 27 stage 4: develop the scenario stories 20, 28–30 stage 5: develop the business strategy 20, 30 scenarios 20 scheduling 258 scroll bars 225, 225 seasonal component 89 seasonal factors 89–90, 90, 91, 93, 94, 94, 96 seed 19, 60, 62, 71, 75, 78, 80, 83 segmentation see under revenue forecasting sensitivity analysis 147, 241–2, 241 shareholder value 193–5, 194, 199 ratio analysis 194–5 short period rate 180 shortcut keys 50–51 sign convention 66, 176 simple modified exponential trend curve 108 SIN function 268–9 SINE curve 71, 76 SMART goals 9 social trends 70 socio-economic shifts 18 specific help software 252 spin buttons 225 splash screens 237–9, 238 spreadsheet applications appearance consistency 229 freezing the screens 229–30, 230 placement of macro buttons 230 279 removing the gridlines 230 simple layout 229 basic programming techniques with Visual Basic 232–6 Forms toolbar 221–5 navigation attaching a macro to a button 228–9, 229 basic navigation 226 creating a menu using Visual Basic 227–8, 227, 228 hyperlinks 226–7, 227 recording simple macros 216 viewing macro code 216–17, 217 printing 231 creating a print macro 231, 231 setting print ranges 231 protecting the model 219–21 spreadsheet functions 263–70 spreadsheets 2, 11 advantages and disadvantages of using 3 and model ownership 35 see also input sheets; output sheets; working sheets start of trade 133, 258 stock 143–4, 144, 202 stock days 143, 144, 202 strategic plan 12, 18, 31 style and outline 59–69 alternative model layout 63–4 formatting 67–9 colours 67 column width 69 fonts 67 lines 67–8, 68 number styles 68–9 making the model intelligible 64 making range names work 64–5, 64 model layout 59–60 recalculation 69 retaining consistent logic by having the same formulae every year 65 rounding to invisible 65–6, 65, 66 sheet layout: inputs 60–61, 60, 61 sheet layout: outputs 63, 63 sheet layout: working 61–2 sign convention 66 some things to avoid, recalculation 69 things to avoid, hiding information 69 sum of the digits 131 SUM function 269 SUM IF function 47–8, 48, 269 supply chain 176 280 SWOT (strengths, weaknesses, opportunities and threats) analysis 257 synergy 176 T tables of data 259–61, 260 tactical plans 18 tasks 10 tax shield on financing 181 taxation 33, 34, 127, 173, 258 the challenges of modelling taxation 163 forms of taxation 163–4, 163 generic approach to corporation taxation workings 164–5, 165, 166–7 technical errors 206 technical obsolescence 131 technological change 70 templates 11, 13, 16, 17, 33 terminal value 14, 189, 258 testing and debugging 33, 34, 206–15 the importance of 206 testing strategy 207–15 step 1: eliminate technical and conceptual flaws 208–12, 214 step 2: range test the model 212–13, 215 step 3: stress test the model 213, 215 step 4: user testing 214, 215 types of errors conceptual errors 206 technical errors 206 user errors 206 text boxes 252 third-party forecasts 70 tick box 43, 43 time frame 13–14, 88 time periods 154–5, 154 time series analysis see under revenue forecasting time value of money 179 top-down forecasting 87–8 total revenue 86, 115–16, 116 trace error button 51 transport trends 15 trend curves, exponential, Gompertz and Logistic 108 TREND function 99, 100, 101, 105, 269 trend see under revenue forecasting trendline 55 regression 98 triangulation 126, 126 U uncertainty, scenario planning and model inputs 19–24 INDEX business model input checklist 24 defining the inputs 19 examining different approaches to uncertainty 19 scenario-based forecasting approach 20 stages of a scenario-based forecasting approach 20, 20 stage 1: identifying high impact, highly uncertain inputs 21–4 analyse variables according to uncertainty and impact 23–4, 23 identify all the variables that influence the business 21–2, 21 identifying the relationships between variables 22 review the data collection requirements 22–3 understanding the nature of uncertainty 19 uncertainty/impact matrix 23–4, 23, 24, 25, 29 units 14 upper asymptote 107, 108, 108 urbanisation 15 useful economic life 131 users documentation 254 errors 206 interfaces 34 support, continuing 255 testing 214 using the model 241–9 dependency ranking 242–4 displaying the assumption dataset on the output sheet 248 Excel Scenario Manager 248 GOAL SEEK 242–4 Monte Carlo analysis 245–8 risk and its management 248–9 sensitivity analysis 241–2 V valuation 60 see also project appraisal and company valuation valuation approaches see project appraisal and company valuation valuation range 190 value-added tax 127 variable costs see under operating costs variables 21–2, 21 dependent 96 endogenous 22 exogenous 22 281 INDEX independent (explanatory) 96–7, 100 uncertainty/impact 23–4, 23 variance analyses 13 version control 35 versions of the model, retaining 35–6 vertical analysis 201 vision statement 18 Visual Basic 216, 232–6 Visual Basic Editor 216–17, 217, 218, 240 VLOOKUP function 121, 122, 269–70 W WACC see weighted average cost of capital warrants 148 warranty 118 weighted average cost of capital (WACC) 152, 167, 180, 181, 190 wind-farm operators critical factors for 15, 16 develop the scenario stories 28–30, 29 Gantt chart 10, 11 impact/uncertainty matrix 23–4, 23 input timelines 29, 29 output template 17 potential input development paths 25–6, 25–6 revenue model 29–30 strategic inputs 30 variables influencing 21, 22 withholding tax 258 working capital see under capital expenditure and working capital working capital turnover 201–2 working sheets 60–5 workshops 17–18 writing and presenting the business plan key issues to address in a business plan 256 presenting the model outputs 259–62 graphs 261, 262 rounding 259 rows versus columns 261 tables of data 259–60 report style 259 typical content of a business plan document assumptions 257–8 commercial risk 257 economic 258 executive summary 257 financial 257 manning 258 market 257 milestones 258 safety, health and environment 258 sensitivity 258 strategic importance 257 taxes 258 technical 258 Z zero, set all inputs to 211 zero book value 136


pages: 566 words: 155,428

After the Music Stopped: The Financial Crisis, the Response, and the Work Ahead by Alan S. Blinder

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Affordable Care Act / Obamacare, asset-backed security, bank run, banking crisis, banks create money, Carmen Reinhart, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, conceptual framework, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, Detroit bankruptcy, diversification, double entry bookkeeping, eurozone crisis, facts on the ground, financial innovation, fixed income, friendly fire, full employment, hiring and firing, housing crisis, Hyman Minsky, illegal immigration, inflation targeting, interest rate swap, Isaac Newton, Kenneth Rogoff, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, market bubble, market clearing, market fundamentalism, McMansion, moral hazard, naked short selling, new economy, Nick Leeson, Northern Rock, Occupy movement, offshore financial centre, price mechanism, quantitative easing, Ralph Waldo Emerson, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, South Sea Bubble, statistical model, the payments system, time value of money, too big to fail, working-age population, yield curve, Yogi Berra

Why interest rates? Because dividends and capital gains received in the future are worth less today when interest rates are higher and more when interest rates are lower. The reason is the time value of money: $1 received later is worth less than $1 received sooner because, if you can get your hands on money sooner, you can put it to work earning interest. When interest rates fall, this difference shrinks. The time value of money becomes less and less important. The reverse happens when interest rates rise. A similar valuation analysis applies to houses, if we ignore emotional attachments and treat buying a house as an investment.

Then the “dividends” you receive are the monthly rental fees you save by owning rather than renting. Since houses last for decades, most of these rental savings come far in the future. So lower interest rates imply higher fundamental values for houses, just as they do for stocks or bonds—and for basically the same reason: the time value of money. The calculation of fundamental value for houses is not quite as straightforward as this, of course. One reason is that huge idiosyncrasies across individual houses make the precise rent that is being “saved” hard to know precisely. (It’s ten o’clock. Do you know how much your house would rent for?)

This fixity of the income stream contrasts starkly with common stocks, where dividends and capital gains rise and fall with the fortunes of companies and are not specified in advance. The fundamental value of a fixed-income security is easy to compute in the absence of default risk: One need compute only the present values of all the future flows of interest and principal, which are fixed and known—and then add them up. Because of the time value of money, lower interest rates make those future flows worth more, implying higher bond prices. For U.S. Treasury bonds, which carry no risk of default, the fundamentals are only the stated (“coupon”) rate of interest and the current market rate of interest. When the market interest rate falls, the bond’s fundamental value rises—and the bond’s value falls when the market interest rate rises.


pages: 624 words: 127,987

The Personal MBA: A World-Class Business Education in a Single Volume by Josh Kaufman

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Albert Einstein, Atul Gawande, Black Swan, business process, buy low sell high, capital asset pricing model, Checklist Manifesto, cognitive bias, correlation does not imply causation, Credit Default Swap, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, Dean Kamen, delayed gratification, discounted cash flows, double entry bookkeeping, Douglas Hofstadter, en.wikipedia.org, Frederick Winslow Taylor, Gödel, Escher, Bach, high net worth, hindsight bias, index card, inventory management, iterative process, job satisfaction, Johann Wolfgang von Goethe, Kevin Kelly, Lao Tzu, loose coupling, loss aversion, market bubble, Network effects, Parkinson's law, Paul Buchheit, Paul Graham, place-making, premature optimization, Ralph Waldo Emerson, rent control, side project, statistical model, stealth mode startup, Steve Jobs, Steve Wozniak, subscription business, telemarketer, the scientific method, time value of money, Toyota Production System, tulip mania, Upton Sinclair, Walter Mischel, Y Combinator, Yogi Berra

A dollar today is worth more than a dollar tomorrow. How much more depends on what you choose to do with that dollar. The more profitable options you have to invest that dollar, the more valuable it is. Calculating the Time Value of Money is a way of making Decisions in the face of Opportunity Costs. Assuming you have various options of investing funds with various returns, the Time Value of Money can help you determine which options to choose and how much you should spend, given the alternatives. Let’s go back to the million dollars example: Assume someone offers you an investment that will deliver $1 million risk free in one year’s time.

Because if you took that amount and invested it in your next best alternative, you’d have a million dollars: $1,000,000 divided by 1.05 (the 5 percent interest/discount rate) equals $952,380. If you can buy the first investment for less than that amount, you’ll be ahead. The Time Value of Money is a very old idea—it was first explained in the early sixteenth century by the Spanish theologian Martín de Azpilcueta. The central insight that a dollar today is worth more than a dollar tomorrow can be extended to apply to many common financial situations. For example, the Time Value of Money can help you figure out the maximum you should be willing to pay for a business that earns $200,000 in profit each year. Assuming an interest rate of 5 percent, no growth, and a foreseeable future of ten years, the “present value” of that series of future cash flows is $1,544,347.

Don’t get bogged down with all of the options available—consider only what appear to be the best alternatives at the time of your decision. If you pay attention to the Opportunity Costs of your decisions, you’ll make much better use of the resources at your disposal. SHARE THIS CONCEPT: http://book.personalmba.com/opportunity-cost/ Time Value of Money They always say time changes things, but you actually have to change them yourself. —ANDY WARHOL, ARTIST Would you rather have a million dollars today or a million dollars five years from now? The answer is obvious: why wait? Having the money now means you can spend it now, or invest it now.


pages: 218 words: 60,935

How to Buy Property at Auction: The Essential Guide to Winning Property and Buy-To-Let Bargains by Samantha Collett

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Firefox, proxy bid, the market place, time value of money

Following due diligence will enable you to make a confident decision about a property purchase – however, there will often still be unknowns and these must be factored into the bid price. Unless a profitable risk to reward ratio exists there is no commercial incentive to buy at auction rather than through an estate agent. 2. Time value of money. The saying: ‘Money today is generally worth more than money tomorrow’, is what is known as the Time Value of Money. The basic statement is very simple: one pound today is worth more than having one pound tomorrow (or next year). The time value of money is a powerful concept in the auction room – and the simple fact is, when you buy property at auction you expect a discount because you are buying today. The money you have in your pocket today should buy you more than it would tomorrow – that is, buying at auction vs. buying with an estate agent.

t. 029 2037 0117 http://www.seelandco.com Ireland Eddisons Ireland t. 00353 1 906 0600 http://www.eddisons.com/ireland Real Estate Alliance t. 00353 1 669 9996 http://www.realestatealliance.ie Allsop Space t. 00353 1 678 9748 http://www.allsopspace.ie Index address and location of property 50, 56–7 Google Maps 62–4 auction blues 197 auction houses 29–43 acting for the vendor 29, 153–4, 155–6 advertisements 38–9 large/medium/small 38–9 list of 224–42 mailing list registration 39, 45–6 mismatched properties 42, 216 specialisation 29–30, 38 statistical sales success 35–8 stock 32–3 auction market, size of (UK) 44–5 auction rooms energy and buzz 52, 148, 150, 172, 215 layout 149–50 positioning yourself in 157–8 psychology of 148–52, 165 auction success checklist 214–15 auction tip journey 215–23 auctioneers 152–6 attracting his/her attention 159–61 code of conduct 155–6 insights and anecdotes 27, 41–2, 54, 79, 95, 103, 138–9, 144, 149, 154, 157, 158, 165, 166 right to sign the contract 183, 185 tactics 153–5 banks commercial lending 102 see also mortgage lenders bargains, extreme 18 bid bid limit 134, 146–7, 151, 197, 221, 222 bid limit, uneven 137, 221 defaulting on 183, 185 increments 163–7, 222 ‘jump’ bids 164, 165, 166 legal and binding 11, 85 making an offer before auction 139–41 ‘off the wall’ 155–6, 222 bid price calculation 105–42 auction discount 129–30 calculation sheet 131–3 hidden buying costs 106–8 selling costs 130–1 see also valuation of property bidding bid pace and opening prices 152 bidding early/late 161–3 by someone else on your behalf 171 deciding not to bid 138, 148, 220 documentation required 145–6 joint purchase 145, 220 online 171–2 pre-bid registration 145–6 proxy bidding 51, 146, 155, 170–1, 172, 220 telephone bidding 51, 149, 155, 168–70, 172, 220 bidding wars 52, 151 ‘blind’, buying 12, 40, 64, 84, 204–5, 210–11 bridging finance 102 builders property assessment and valuation 89–90 quotes 125, 126 buy-to-let 6, 101 buyers characteristics 5–6 types of 40–1 buyer’s premium 107, 168 buying after auction 175–7, 203–4, 223 buying before auction 139–41 capital yield 136–7 cash buyers 44, 103 catalogues 46, 48–53, 178 amendments 143–4, 182, 221 entries 50–1 online 46 property descriptions 50, 57, 216 see also lots and lot numbers certainty of sale 23–5 cheque payments 145, 186 clawback conditions 94 commercial lending 102 competition 158, 161 completion 21, 186–92 deadline 21–2, 99–100, 201, 223 delays 190 failure to complete 100, 191, 223 longer completion times 103, 219 conditions of sale 58, 155, 193 contract legally binding 28, 100, 183, 193–4 Memorandum of Contract 23, 184, 185, 187 rescinding 194, 223 contract law 195 conveyancing legal fees 107 costing renovation works 120–8 builders’ quotes 125, 126, 189, 220 contingency sums 126 costing your time 126–8 planning works 120–2 schedule of works 122–5 council tax 190 crime-mapping 118 damps, signs of 73 deposit 99, 168 forfeit of 100, 188, 191 ‘dream team’ of experts 103, 218 electrics, checking 72–3 Energy Performance Certificate (EPC) 65, 95 environmental hazards 119 Essential Information Group (EIG) 45 estate agents 69 buying property through 23–4, 25, 26, 47, 48, 85 networking with 113, 190 online estate agents 131 property valuations 113–17 selling property through 33, 96, 131 Estates Gazette 45 ex-council properties see local authority disposals exchange of contracts 99, 139, 175, 183–6 exterior of property, checking 73–4 falling property prices, tracking 111–12 finance 99–103, 187–8, 219 bridging finance 102 cash 103 cleared funds 99, 145, 146, 171, 186 commercial lending 102 costs of raising finance 107–8 deposit 99, 168 mortgage see mortgage Plan B 100, 200, 219 proof of funding 47 financial charges registered against a property 66 finding an auction property auction house mailing lists 45–6 professional subscription 45 publications 45 search alerts 83, 216 fines and penalties for delay/failure to complete 100, 190–1, 209 ‘flipping’ 130 Google Maps 62–4 guide price 10, 18, 26, 50–1, 55–6 and reserve price, relation between 55–6 ‘hawking’ 175 homebuyer report 87, 88, 89 ‘hooks’ 52 house price indexes 112–13 housing associations 33, 38, 39 institutional investors 34, 38 insurance 108, 187 investment property 14, 15–16, 136 see also property investors; tenanted property jargon 10–11 Land Registry data 65, 66, 70, 110, 111, 112 leasehold property ground rents 93 insurance 187 lease, length of 66, 93, 115, 218 legal fees 107 service charges 66, 93 title plan and title deeds 65–6, 93–4 viewing 74 legal documents 90–8 delayed/incomplete 178, 218 downloading 65, 91–2 legal pack 91–2 pre-bid checks 65–6, 91, 93–7 special conditions 94, 95, 218 see also contract legal expenses conveyancing work 107 seller’s costs, contribution to 94, 107, 212–13, 218 legal property problems 96–9 local area knowledge 40, 114, 117–20 local authority disposals 27, 33, 75, 94, 139 local searches 94 locks, changing 190 lots and lot numbers 10, 49 ‘hooks’ 52 order of 51, 52, 216 ‘reverse hooks’ 52 market value 26, 27, 34, 55, 216 Memorandum of Contract 23, 184, 185, 187 meter readings 190 misrepresentation and misdescription 194–6 money laundering rules 44 mortgage 101 ‘approved in principle’ 100, 101 fees 107–8 habitable property test 101, 102, 219 mortgage valuation 86, 87, 88, 89, 101 mortgage lenders mortgage refusal 66–7 selling property at auction 27, 33, 39 neighbourhood profile 117–18 neighbours, talking to 74, 217 online resources legal documents 65, 91–2 local area knowledge 117–19 price trends 112–13 property details 83 property websites 110–12 search alerts 83, 216 watching auctions live 45 outbid at auction 197–200, 201, 223 owner-occupation, buying for 8–9, 41, 121, 199–200 paddle system 146 parking facilities, checking 74, 115 payment cash buyers 44, 103 cheques, cards, bankers’ drafts 145 cleared funds 99, 145, 146, 171, 186 photographs (catalogue entries) 50, 56 planning applications and consents 74, 119 plumbing, checking 72 preparation 58, 85–104 finance 99–103 legal documents 90–8 surveys 86–90 price auction discount 18, 129–30 ceiling price 121 guide price 10, 18, 26, 50–1, 55–6 house price indexes 112–13 reserve price 10, 55–6, 140–1, 156, 175, 222 trends 112–13 see also bid price calculation; valuation of property private vendors 33, 34, 39, 140 professional subscription 45 Property Auction News 45 property developers 40 property investment companies 34 property investors 40 property owning culture 6 property title 65–6, 93–4 unregistered or complicated 97 property traders 40 proxy bidding 51, 146, 155, 170–1, 220 publications 45 reasons for buying property at auction 12–28 reasons for selling property at auction 75–7, 79, 217 refurbishment/renovation cash flow 189 cost effectiveness 116–17, 121–2, 220 costing works 120–8 doing it yourself 126–9 overspend 121 planning works 120–2 repossessed properties 46–7 schedule of works 122–5, 220 Registers of Scotland 110, 112 rental yields 40, 136, 137 over-inflated/unrealistic 94 repossessions 13, 15, 46–8 best possible price, lender’s obligation to achieve 27, 33, 46, 139 estate agents’marketing of 33, 47, 48 exchange and completion timescale 22, 47 finding 47 refurbishment 46–7 research pre-bidding research 85, 173–4 pre-viewing research 62–7, 69–70 property market 109–19 see also online resources reserve price 10, 55–6, 140–1, 156, 222 failure to meet 175 ‘reverse hooks’ 52 risk to reward ratio 129, 134 roof, checking 72 sale day 143–82, 220–1 auction fever 151 auction nerves 147–8 practice run 172–4 see also auction rooms; bidding school inspection reports and league tables 119 search alerts 83, 216 sellers at auction 33–5 less than six-month ownership of property 66–7, 219 selling on property, costs 130–1 sold property prices data 110–11 solicitors and completion of sale 96, 187, 188 fees 96 pre-bidding check of legal documents 95–7, 218 spotters 159 Stamp Duty Land Tax (SDLT) 106 stock (auction houses) 11, 32–3, 38, 39, 42 Streetview 63–4 structural soundness, checking 73 surveys 82, 86–90, 188, 218 builder’s evaluation 89–90 condition report/mortgage valuation 86, 87, 88, 89, 101 costs 88–9, 108 friends, second opinions from 90 full structural survey 88, 89 homebuyer report 87, 88, 89 own survey 71–4 verbal report 89 telephone bidding 51, 149, 155, 168–70, 220 tenanted property 92–3, 189 assured shorthold tenancies 94 regulated tenancies 94 rental yields 40, 94, 136, 137 viewing 81, 82 time value of money 130 timeframe 21–2 title plan and deeds 65–6, 70, 93–4 ‘too good to be true’ property 57–8, 104, 217 transparent process 25–7, 216 transport links 118 unmodernised property 13, 15 see also refurbishhment/renovation ‘unsafe’ properties 82 unsold property 174–7, 223 unusual properties 15, 30–1, 75 valuation of property ceiling price 121, 219 costing works 120–8 end value after renovation 108, 122, 126 estate agents’ knowledge 113–17 in current condition 108, 109 local area knowledge 114, 117–20 margin 109, 126, 133–5, 220 online tools 110, 111, 219 property market research 109–19 property price trends 112–13 property website information 110–12 variety of properties 13–17 VAT 94, 107 viewing 59–82, 216–17 arrangements 51, 59–60 block viewings 59, 60, 61–2, 83 checklist of key areas 71–4 duration 70 internal viewings unavailable 81–2 key items to take on a 71 pre-viewing research 62–7, 69–70 sense checks 77–9 successful 69–70 viewing company services 60 viewing slots 59, 60 withdrawn property 177–80 written enquiries 58 yields 135–7 capital yield 136–7 rental yield 40, 136, 137


pages: 77 words: 18,414

How to Kick Ass on Wall Street by Andy Kessler

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Andy Kessler, Bernie Madoff, buttonwood tree, call centre, collateralized debt obligation, family office, fixed income, hiring and firing, invention of the wheel, invisible hand, London Whale, margin call, NetJets, Nick Leeson, pets.com, risk tolerance, Silicon Valley, sovereign wealth fund, time value of money, too big to fail, value at risk

Pretty simple - how to generate revenue and create long term value for your firm. A friend of mine who worked on Wall Street from the day he graduated college told me there are two important things to learn to be able to generate revenue and long term value. The first is to understand the time value of money. Everything begins and ends with the cost of financing. Doesn’t matter if you are a trader, investment banker, salesman or in research, this time value of money is critical. If you don’t understand this, no one will provide you any capital to make more money. To do this right, you have to understand how to get capital, but how money flows in the capital markets, how it hops between market players and how to insert yourself in this flow.


pages: 444 words: 86,565

Investment Banking: Valuation, Leveraged Buyouts, and Mergers and Acquisitions by Joshua Rosenbaum, Joshua Pearl, Joseph R. Perella

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asset allocation, asset-backed security, bank run, barriers to entry, capital asset pricing model, collateralized debt obligation, corporate governance, credit crunch, discounted cash flows, diversification, fixed income, London Interbank Offered Rate, performance metric, shareholder value, sovereign wealth fund, technology bubble, time value of money, transaction costs, yield curve

CALCULATE PRESENT VALUE AND DETERMINE VALUATION Calculate Present Value Calculating present value centers on the notion that a dollar today is worth more than a dollar tomorrow, a concept known as the time value of money. This is due to the fact that a dollar earns money through investments (capital appreciation) and/or interest (e.g., in a money market account). In a DCF, a company’s projected FCF and terminal value are discounted to the present at the company’s WACC in accordance with the time value of money. The present value calculation is performed by multiplying the FCF for each year in the projection period and the terminal value by its respective discount factor.

For example, assuming a sponsor contributes $250 million of equity and receives equity proceeds of $750 million at the end of the investment horizon, the cash return is 3.0x (assuming no additional investments or dividends during the period). However, unlike IRR, the cash return approach does not factor in the time value of money. How LBOs Generate Returns LBOs generate returns through a combination of debt repayment and growth in enterprise value. Exhibit 4.6 depicts how each of these scenarios independently increases equity value, assuming a sponsor purchases a company for $1,000 million, using $750 million of debt financing (75% of the purchase price) and an equity contribution of $250 million (25% of the purchase price).

As we progress through the projection period, equity value increases due to the increasing EBITDA and decreasing net debt. Therefore, the cash return increases as it is a function of the fixed initial equity investment and increasing equity value at exit. In ValueCo’s case, however, as the timeline progresses, IRR decreases in accordance with the declining growth rates and the time value of money. IRR Sensitivity Analysis Sensitivity analysis is critical for analyzing IRRs and framing LBO valuation. IRR can be sensitized for several key value drivers, such as entry and exit multiple, exit year, leverage level, and equity contribution percentage, as well as key operating assumptions such as growth rates and margins (see Chapter 3, Exhibit 3.59).


pages: 408 words: 85,118

Python for Finance by Yuxing Yan

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asset-backed security, business intelligence, capital asset pricing model, constrained optimization, correlation coefficient, distributed generation, diversified portfolio, implied volatility, market microstructure, P = NP, p-value, quantitative trading / quantitative finance, Sharpe ratio, time value of money, value at risk, volatility smile

80 Importing a module 80 Adopting a short name for an imported module 81 Showing all functions in an imported module 82 Comparing "import math" and "from math import *" 82 Deleting an imported module 83 Importing only a few needed functions 84 Finding out all built-in modules 85 Finding out all the available modules 86 Finding the location of an imported module 87 More information about modules 88 Finding a specific uninstalled module 90 Module dependency 90 Summary 92 Exercises 93 Installation of NumPy and SciPy Launching Python from Anaconda Examples of using NumPy Examples of using SciPy Showing all functions in NumPy and SciPy More information about a specific function Understanding the list data type Working with arrays of ones, zeros, and the identity matrix Performing array manipulations Performing array operations with +, -, *, / Performing plus and minus operations [ iii ] 96 96 97 98 102 103 103 104 105 105 105 Table of Contents Performing a matrix multiplication operation 105 Performing an item-by-item multiplication operation 107 The x.sum() dot function 107 Looping through an array 108 Using the help function related to modules 108 A list of subpackages for SciPy 109 Cumulative standard normal distribution 109 Logic relationships related to an array 110 Statistic submodule (stats) from SciPy 111 Interpolation in SciPy 112 Solving linear equations using SciPy 113 Generating random numbers with a seed 114 Finding a function from an imported module 116 Understanding optimization 116 Linear regression and Capital Assets Pricing Model (CAPM) 117 Retrieving data from an external text file 118 The loadtxt() and getfromtxt() functions 118 Installing NumPy independently 119 Understanding the data types 119 Summary 120 Exercises 120 Chapter 7: Visual Finance via Matplotlib Installing matplotlib via ActivePython Alternative installation via Anaconda Understanding how to use matplotlib Understanding simple and compounded interest rates Adding texts to our graph Working with DuPont identity Understanding the Net Present Value (NPV) profile Using colors effectively Using different shapes Graphical representation of the portfolio diversification effect Number of stocks and portfolio risk Retrieving historical price data from Yahoo! Finance Histogram showing return distribution Comparing stock and market returns Understanding the time value of money Candlesticks representation of IBM's daily price Graphical representation of two-year price movement IBM's intra-day graphical representations [ iv ] 123 124 125 125 129 131 133 135 137 139 140 142 144 145 148 150 151 153 154 Table of Contents Presenting both closing price and trading volume 156 Adding mathematical formulae to our graph 157 Adding simple images to our graphs 158 Saving our figure to a file 159 Performance comparisons among stocks 160 Comparing return versus volatility for several stocks 161 Finding manuals, examples, and videos 163 Installing the matplotlib module independently 163 Summary 163 Exercises 164 Chapter 8: Statistical Analysis of Time Series Installing Pandas and statsmodels Launching Python using the Anaconda command prompt Launching Python using the DOS window Launching Python using Spyder Using Pandas and statsmodels Using Pandas Examples from statsmodels Open data sources Retrieving data to our programs Inputting data from the clipboard Retrieving historical price data from Yahoo!

Otherwise, we reject it, as given in the following conditions:  If Payback ( project ) < Tcritical accept   If Payback ( project ) > Tcritical reject [ 60 ] (16) Chapter 3 Compared with the NPV rule, the payback period rule has many shortcomings, including the fact that it ignores the time value of money and cash flows after the payback period, and the benchmark of the critical value is ad hoc. The advantage is that this rule is very simple. Defining IRR and the IRR rule IRR is the discount rate resulting in a zero NPV. The IRR rule is that if our project's IRR is bigger than our cost of capital, we accept the project.

Then estimate their returns and represent them via a graph using the following code: from matplotlib.pyplot import * from matplotlib.finance import quotes_historical_yahoo import numpy as np def ret_f(ticker,begdate,enddate): p = quotes_historical_yahoo(ticker, begdate, enddate,asobject=True, adjusted=True) return((p.aclose[1:] - p.aclose[:-1])/p.aclose[:-1]) begdate=(2013,1,1) enddate=(2013,2,9) ret1=ret_f('IBM',begdate,enddate) ret2=ret_f('^GSPC',begdate,enddate) n=min(len(ret1),len(ret2)) [ 148 ] Chapter 7 s=np.ones(n)*2 t=range(n) line=np.zeros(n) plot(t,ret1[0:n], 'ro',s ) plot(t,ret2[0:n], 'bd',s) plot(t,line,'b',s) figtext(0.4,0.8,"Red for IBM, Blue for S&P500") xlim(1,n) ylim(-0.04,0.07) title("Comparions between stock and market retuns") xlabel("Day") ylabel("Returns") show() The output corresponding to the preceding code is given as follows: [ 149 ] Visual Finance via Matplotlib Understanding the time value of money In finance, we know that $100 received today is more valuable than $100 received one year later. If we use size to represent the difference, we could have the following Python program to represent the same concept: from matplotlib.pyplot import * fig1 = figure(facecolor='white') ax1 = axes(frameon=False) ax1.set_frame_on(False) ax1.get_xaxis().tick_bottom() ax1.axes.get_yaxis().set_visible(False) x=range(0,11,2) x1=range(len(x),0,-1) y = [0]*len(x); annotate("Today's value of $100 received today",xy=(0,0),xytext=(2,0.001) ,arrowprops=dict(facecolor='black',shrink=0.02)) annotate("Today's value of $100 received in 2 years",xy=(2,0.00005),xytex t=(3.5,0.0008),arrowprops=dict(facecolor='black',shrink=0.02)) annotate("received in 6 years",xy=(4,0.00005),xytext=(5.3,0.0006),arrowpr ops=dict(facecolor='black',shrink=0.02)) annotate("received in 10 years",xy=(10,-0.00005),xytext=(4,-0.0006),arrow props=dict(facecolor='black',shrink=0.02)) s = [50*2.5**n for n in x1]; title("Time value of money ") xlabel("Time (number of years)") scatter(x,y,s=s); show() The output graph is shown as follows: [ 150 ] Chapter 7 Candlesticks representation of IBM's daily price We could use candlesticks to represent the daily opening, high, low, and closing prices.


pages: 376 words: 109,092

Paper Promises by Philip Coggan

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accounting loophole / creative accounting, balance sheet recession, bank run, banking crisis, barriers to entry, Berlin Wall, Bernie Madoff, Black Swan, Bretton Woods, British Empire, call centre, capital controls, Carmen Reinhart, carried interest, Celtic Tiger, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, debt deflation, delayed gratification, diversified portfolio, eurozone crisis, Fall of the Berlin Wall, falling living standards, fear of failure, financial innovation, financial repression, fixed income, floating exchange rates, full employment, German hyperinflation, global reserve currency, hiring and firing, Hyman Minsky, income inequality, inflation targeting, Isaac Newton, joint-stock company, Kenneth Rogoff, labour market flexibility, Long Term Capital Management, manufacturing employment, market bubble, market clearing, Martin Wolf, money: store of value / unit of account / medium of exchange, moral hazard, mortgage debt, Nick Leeson, Northern Rock, oil shale / tar sands, paradox of thrift, peak oil, pension reform, Plutocrats, plutocrats, Ponzi scheme, price stability, principal–agent problem, purchasing power parity, quantitative easing, QWERTY keyboard, railway mania, regulatory arbitrage, reserve currency, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Reagan, savings glut, short selling, South Sea Bubble, sovereign wealth fund, special drawing rights, The Chicago School, The Great Moderation, The Wealth of Nations by Adam Smith, time value of money, too big to fail, trade route, tulip mania, value at risk, Washington Consensus, women in the workforce

In modern times, investors have the option of lending to their government, a choice that has often been regarded as ‘risk-free’, even though that term looks rather hollow in the light of the sovereign debt crisis. Still if a country goes bust, it is likely that its consumers and companies will also be in trouble; it is rational for creditors to demand a higher rate from private-sector borrowers than from their government. Lenders also need to be rewarded for the time value of money. It is natural to prefer having $1,000 today to having $1,000 in a year’s time, not least because the price of goods might rise in the interim. Interest rates will thus naturally be higher when inflation is high. This need not necessarily be bad for the debtor, since their incomes will be growing rapidly as well in inflationary times.

Instalment selling greatly widened the potential market for a retailer’s goods, and the financing charges more than offset any bad debts. In practice, one wonders if the approach was really that much different from the old habit of allowing customers to buy ‘on the slate’. Presumably such retailers marked their prices higher to allow for both the time value of money and the occasional bad debts. Psychologically, however, it was an important step forward. Consumers liked the ability to get their goods upfront and found the prospect of a series of small payments easy to swallow, even though they ended up paying more for the goods in the end. Instalment credit had other advantages for the retailer, especially when compared with outright credit.

The Implications of Long-term Shifts in Global Investment and Saving’, McKinsey Global Institute, December 2010. 18 The figures are based on ten mature economies and four developing economies (Brazil, China, India and Mexico). 19 This argument relies on the discounted cashflow approach to valuation. The value of an asset is equal to the future cashflows, discounted to allow for the time value of money. A lower discount rate thus means a higher present value. This argument is a little short-sighted, however. Low real rates should be a sign of low expected growth. So to the extent that the discount rate falls, expected future cashflows should fall as well. 20 Grantham, ‘Night of the Living Fed’. 8.

Early Retirement Guide: 40 is the new 65 by Manish Thakur

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Airbnb, diversified portfolio, financial independence, index fund, Lyft, passive income, passive investing, risk tolerance, Robert Shiller, Robert Shiller, time value of money, Vanguard fund, Zipcar

Live a month off of a strictly set amount of money without using any extra. 2. After living for a few months, try increasing your automatic investing contribution by 5% - 10%, even if you have to get rid something like the morning coffee from the store. Keep the Investing Inertia Going Take advantage of the Time Value of Money. This is a finance term that means $1 today is actually worth more than $1 tomorrow. When you have money to save in the present, it has opportunities to be invested in accounts and opportunities that will pay off interest each year and grow. $1,000 invested at 7% over the next 40 years is worth $14,974.46, whereas the same $1,000 in the same account for 35 years is only $10,676.58, nearly a $5,000 difference!

The Concepts and Practice of Mathematical Finance by Mark S. Joshi

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Black-Scholes formula, Brownian motion, correlation coefficient, Credit Default Swap, delta neutral, discrete time, Emanuel Derman, implied volatility, incomplete markets, interest rate derivative, interest rate swap, London Interbank Offered Rate, martingale, millennium bug, quantitative trading / quantitative finance, short selling, stochastic process, stochastic volatility, the market place, time value of money, transaction costs, value at risk, volatility smile, yield curve, zero-coupon bond

In conclusion, in return for the £1 deposit at the start of the FRA, the company receives X = (1 + ro)-to(l + t.r)ri at the end. One can then convert this into an equivalent compounding annual interest rate, 1'2, by solving (1+1.2)11-'0=X. 2.6 The time value of money The second important aspect of pricing the forward contract is the concept of time value of money. Jam today is better than jam tomorrow - an investor will prefer a pound in his pocket today to a pound in his pocket one year from now. In effect, a pound a year from now is therefore worth less than a pound today. The interest paid on a riskless loan expresses this.

1.2 Market efficiency 1.3 The most important assets 1.4 Risk diversification and hedging 1.5 The use of options 1.6 Classifying market participants 1.7 Key points 1.8 Further reading 1.9 Exercises 2 Pricing methodologies and arbitrage 2.1 Some possible methodologies 2.2 Delta hedging 2.3 What is arbitrage? 2.4 The assumptions of mathematical finance 2.5 An example of arbitrage-free pricing 2.6 The time value of money 2.7 Mathematically defining arbitrage 2.8 Using arbitrage to bound option prices 2.9 Conclusion 2.10 Key points 2.11 Further reading 2.12 Exercises 3 Trees and option pricing 3.1 A two-world universe 3.2 A three-state model vii Contents viii Multiple time steps Many time steps A normal model Putting interest rates in A log-normal model Consequences Summary 3.10 Key points 3.11 Further reading 3.12 Exercises Practicalities 4.1 Introduction 4.2 Trading volatility 4.3 Smiles 4.4 The Greeks 4.5 Alternative models 4.6 Transaction costs 4.7 Key points 4.8 Further reading 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.9 5 6 Exercises The Ito calculus Introduction 5.1 Brownian motion 5.2 5.3 Quadratic variation 5.4 Stochastic processes 5.5 Ito's lemma 5.6 Applying Ito's lemma 5.7 An informal derivation of the Black-Scholes equation 5.8 Justifying the derivation 5.9 Solving the Black-Scholes equation 5.10 Dividend-paying assets 5.11 Key points 5.12 Further reading 5.13 Exercises Risk neutrality and martingale measures 50 53 55 58 60 68 70 70 71 71 73 73 73 74 77 85 90 90 91 91 97 97 97 100 102 106 111 114 116 119 121 123 125 125 127 6.1 Plan 127 6.2 6.3 6.4 6.5 Introduction The existence of risk-neutral measures The concept of information Discrete martingale pricing 128 129 140 145 Contents 7 Continuous martingales and filtrations 6.6 6.7 Identifying continuous martingales 6.8 Continuous martingale pricing 6.9 Equivalence to the PDE method 6.10 Hedging 6.11 Time-dependent parameters 6.12 Completeness and uniqueness 6.13 Changing numeraire 6.14 Dividend-paying assets 6.15 Working with the forward 6.16 Key points 6.17 Further reading 6.18 Exercises The practical pricing of a European option Introduction 7.1 Analytic formulae 7.2 7.3 8 9 Trees Numerical integration 7.4 Monte Carlo 7.5 7.6 PDE methods 7.7 Replication 7.8 Key points 7.9 Further reading 7.10 Exercises Continuous barrier options Introduction 8.1 8.2 The PDE pricing of continuous barrier options 8.3 Expectation pricing of continuous barrier options 8.4 The reflection principle 8.5 Girsanov's theorem revisited 8.6 Joint distribution 8.7 Pricing continuous barriers by expectation 8.8 American digital options Key points 8.9 8.10 Further reading 8.11 Exercises Multi-look exotic options 9.1 Introduction 9.2 Risk-neutral pricing for path-dependent options 9.3 Weak path dependence ix 154 156 157 161 162 164 166 167 171 172 175 176 176 181 181 182 183 187 191 195 196 198 198 199 202 202 205 207 208 210 213 216 219 220 220 220 222 222 223 225 Contents x 10 11 12 Path generation and dimensionality reduction Moment matching Trees, PDEs and Asian options Practical issues in pricing multi-look options Greeks of multi-look options Key points Further reading 9.10 Exercises 9.11 Static replication 10.1 Introduction 10.2 Continuous barrier options 10.3 Discrete barriers 10.4 Path-dependent exotic options 10.5 The up-and-in put with barrier at strike 10.6 Put-call symmetry 10.7 Conclusion and further reading 10.8 Key points 10.9 Exercises Multiple sources of risk 11.1 Introduction 11.2 Higher-dimensional Brownian motions 11.3 The higher-dimensional Ito calculus 11.4 The higher-dimensional Girsanov theorem 11.5 Practical pricing 11.6 The Margrabe option 11.7 Quanto options 11.8 Higher-dimensional trees 11.9 Key points 11.10 Further reading 11.11 Exercises Options with early exercise features 12.1 Introduction 12.2 The tree approach 12.3 The PDE approach to American options 12.4 American options by replication 12.5 American options by Monte Carlo 12.6 Upper bounds by Monte Carlo 12.7 Key points 12.8 Further reading 12.9 Exercises 9.4 226 9.5 9.6 9.7 9.8 9.9 231 233 234 236 239 239 240 243 243 244 247 249 251 252 256 258 259 260 260 261 263 267 272 273 275 277 280 281 281 284 284 287 289 291 293 295 297 297 298 Contents 13 14 Interest rate derivatives 13.1 Introduction 13.2 The simplest instruments 13.3 Caplets and swaptions 13.4 Curves and more curves 13.5 Key points 13.6 Further reading 13.7 Exercises The pricing of exotic interest rate derivatives 14.1 Introduction 14.2 Decomposing an instrument into forward rates 14.3 Computing the drift of a forward rate 14.4 The instantaneous volatility curves 14.5 The instantaneous correlations between forward rates Doing the simulation Rapid pricing of swaptions in a BGM model Automatic calibration to co-terminal swaptions Lower bounds for Bermudan swaptions Upper bounds for Bermudan swaptions Factor reduction and Bermudan swaptions Interest-rate smiles Key points Further reading Exercises Incomplete markets and jump-diffusion processes 15.1 Introduction 15.2 Modelling jumps with a tree 15.3 Modelling jumps in a continuous framework 15.4 Market incompleteness 15.5 Super- and sub-replication 15.6 Choosing the measure and hedging exotic options 15.7 Matching the market 15.8 Pricing exotic options using jump-diffusion models 15.9 Does the model matter?

The cost of bonds is generally quoted in terms of yield, that is, the effective annually compounded interest rate which would give the same value on maturity. If the yield is r which could be a number written as 0.05, or more often as 5%, and the bond runs for T years then £1 invested in it today will be worth £(1 + r) after a year and because of compounding £(l. + after two 2.6 The time value of money 25 years and so. In particular, after 7' years, it will be worth £(l + r)T . Similarly, £1 in T years from now will be worth £(1 +).)-T today. To see this, consider that we can take out a loan of £(1-i- r)-T today with the knowledge that we can pay off the loan with the £1 when it arrives.


pages: 447 words: 104,258

Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues by Alain Ruttiens

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algorithmic trading, asset allocation, asset-backed security, backtesting, banking crisis, Black Swan, Black-Scholes formula, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, discrete time, diversification, fixed income, implied volatility, interest rate derivative, interest rate swap, margin call, market microstructure, martingale, p-value, passive investing, quantitative trading / quantitative finance, random walk, risk/return, Sharpe ratio, short selling, statistical model, stochastic process, stochastic volatility, time value of money, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-coupon bond

However, for “marketing” reasons (and misuse of language), it happens that many operations are abusively qualified as “arbitrage”, though they are in fact purely speculative; but the speculator is more or less convinced that his operation will give rise to a profit, based on the difference between observed market prices and his own evaluation of an adequate fair value. Typical examples involve some derivatives hard to price theoretically, such as credit derivatives, some exotic options, and so on. FURTHER READING Pamela PETERSON-DRAKE, Frank J. FABOZZI, Foundations and Applications of the Time Value of Money, John Wiley & Sons, Inc., Hoboken, 2009, 298 p. Paul FAGE, Yield Calculations, CSFB, 1986, 134 p. 1. This is to show that day count conventions may vary even in the same currency. Swaps and swap rates are studied in Chapter 6. 2. Yield curves are studied in Chapter 2. Here we just compare “rough” curves of joined discount factors and of zeroes. 3.

NEFTCI, An Introduction to the Mathematics of Financial Derivatives, Academic Press, 2nd ed., 2000, 527 p. Roger B. NELSEN, An Introduction to Copulas, Springer, 2010, 284 p. Adel OSSEIRAN, Mohamed BOUZOUBAA, Exotic Options and Hybrids, John Wiley & Sons, Ltd, Chichester, 2010, 392 p. Pamela PETERSON-DRAKE, Frank J. FABOZZI, Foundations and Applications of the Time Value of Money, John Wiley & Sons, Inc., Hoboken, 2009, 298 p. S.T. RACHEV, S.V. STOYANOV, F.J. FABOZZI, A Probability Metrics Approach to Financial Risk Measures, Wiley-Blackwell, 2011, 355 p. Riccardo REBONATO, Volatility and Correlation: The Perfect Hedger and the Fox, John Wiley & Sons, Ltd, Chichester, 2nd ed., 2004, 864 p.


pages: 349 words: 134,041

Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives by Satyajit Das

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accounting loophole / creative accounting, Albert Einstein, Asian financial crisis, asset-backed security, Black Swan, Black-Scholes formula, Bretton Woods, BRICs, Brownian motion, business process, buy low sell high, call centre, capital asset pricing model, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, currency peg, disintermediation, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, Haight Ashbury, high net worth, implied volatility, index arbitrage, index card, index fund, interest rate derivative, interest rate swap, Isaac Newton, job satisfaction, locking in a profit, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Marshall McLuhan, mass affluent, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, mutually assured destruction, new economy, New Journalism, Nick Leeson, offshore financial centre, oil shock, Parkinson's law, placebo effect, Ponzi scheme, purchasing power parity, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk-adjusted returns, risk/return, shareholder value, short selling, South Sea Bubble, statistical model, technology bubble, the medium is the message, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, volatility smile, yield curve, Yogi Berra, zero-coupon bond

Now, we can work out a reasonable value of the option – the expected value. This is simply the value of the option multiplied by the probability that the option will be worth that. See Table 6.2. The expected value of the call option in this case is $4 in one year from now. We adjust for the fact that we get $4 in one year for the time value of money. We discount back the $4 at 10.00% pa for one year. This gives us $3.64, the value of the option today. DAS_C07.QXP 8/7/06 4:45 PM 192 Page 192 Tr a d e r s , G u n s & M o n e y Table 6.2 N Option expected value Expected share price in one year Probability $90 $100 $110 $120 $130 10% 20% 40% 20% 10% Value of call option at maturity Expected value (probability × value of call option at maturity) 0 0 0 $10 $20 0 0 0 $2 $2 Total $4 This does not mean that if we buy the option we always get $4.

With the exchangeable, the shares were only sold for tax purposes when the bond converted. This generally takes place towards the final maturity of the convertible. In effect, the exchangeable allowed IBM to defer its tax bill on any gain on the Intel shares. If you can’t evade tax, then you try and defer it for as long as possible. It’s all about the time value of money and taxes. In the 1990s, the process of monetization became more brazen. The stock boom meant that investors were sitting on large gains. They wanted to lock in the gains but defer the tax. DAS_C04.QXP 8/7/06 4:51 PM Page 261 8 N S h a re a n d s h a re a l i k e – d e r i v a t i v e i n e q u i t y 261 There was also a different constituency.

Investment: A History by Norton Reamer, Jesse Downing

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Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Berlin Wall, Bernie Madoff, Brownian motion, buttonwood tree, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, equity premium, estate planning, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, family office, Fellow of the Royal Society, financial innovation, fixed income, Gordon Gekko, Henri Poincaré, high net worth, index fund, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, means of production, Menlo Park, merger arbitrage, moral hazard, mortgage debt, Network effects, new economy, Nick Leeson, Own Your Own Home, pension reform, Ponzi scheme, price mechanism, principal–agent problem, profit maximization, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sand Hill Road, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, technology bubble, The Wealth of Nations by Adam Smith, time value of money, too big to fail, transaction costs, underbanked, Vanguard fund, working poor, yield curve

This was particularly true with respect to lending, which was usually burdened with moralistic concepts, sometimes unfortunate and economically counterproductive. As pointed out later in this chapter, blanket concepts of “usurious” lending often failed to recognize such now-basic issues as the time value of money and credit risk. In addition, social standing and status frequently entered into economic transactions in ways that current civilizations ignore or explicitly reject. Further, at times religious groups and orders engaged in commercial activity in ways that are much less common today, bringing concepts of theology and morality to the forefront of economic dealings in ways that are no longer considered to be pertinent.

The advent of laws and regulations against usury has been a striking and probably destructive element for investment. While there are circumstances that argue against permitting powerful lenders to take advantage of relatively weak and defenseless borrowers, modern Westerners do not usually object to incorporating proper credit and time value risk. In our modern worldview, “time value of money” should have a price. Providing money to another person or organization means that the lender gives up access to that money for a period of time and accepts the risk of loss. Furthermore, the fairness of that price cannot A Privilege of the Power Elite 33 be measured exclusively in proportion to the level of interest charged.


pages: 186 words: 49,251

The Automatic Customer: Creating a Subscription Business in Any Industry by John Warrillow

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Airbnb, airport security, Amazon Web Services, asset allocation, barriers to entry, call centre, cloud computing, discounted cash flows, high net worth, Jeff Bezos, Network effects, passive income, rolodex, sharing economy, side project, Silicon Valley, Silicon Valley startup, software as a service, statistical model, Steve Jobs, Stewart Brand, subscription business, telemarketer, time value of money, Zipcar

Let’s take a closer look at how your company is valued without a subscription offering. In my experience, the most common methodology used to value a small to mid-size business is called discounted cash flow. This methodology forecasts your future stream of profits and then “discounts” it back to what your future profit is worth to an investor in today’s dollars given the time value of money. This investment theory may sound like MBA talk, but discounted cash flow valuation is something you have likely applied in your own personal life without knowing it. For example, what would you pay today for an investment that you hope will be worth $100 one year from now? You would likely “discount” the $100 by your expectation for a return on investment.


pages: 263 words: 75,455

Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors by Wesley R. Gray, Tobias E. Carlisle

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Albert Einstein, Andrei Shleifer, asset allocation, Atul Gawande, backtesting, Black Swan, capital asset pricing model, Checklist Manifesto, cognitive bias, compound rate of return, corporate governance, correlation coefficient, credit crunch, Daniel Kahneman / Amos Tversky, discounted cash flows, Eugene Fama: efficient market hypothesis, forensic accounting, hindsight bias, Louis Bachelier, p-value, passive investing, performance metric, quantitative hedge fund, random walk, Richard Thaler, risk-adjusted returns, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, statistical model, systematic trading, The Myth of the Rational Market, time value of money, transaction costs

This simple principle was first described in 1934 by John Burr Williams in his Theory of Investment Value.4 Williams's principle gives us the discounted cash flow (DCF) analysis, which allows us to calculate intrinsic value by taking a series of growing future cash flows and discounting them back to the present at a rate of return that takes into account the time value of money and the particular risk of the business analyzed. More recently, academics and practitioners alike have come to recognize the significance of Buffett's observation that the value of a business depends on its ability to generate returns on invested capital in excess of its cost of capital.5 Businesses expected to produce returns on invested capital in excess of market rates of return are worth more than the capital invested in them, and the market price of the stock should in time exceed its asset value.

Raw Data Is an Oxymoron by Lisa Gitelman

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collateralized debt obligation, computer age, continuous integration, crowdsourcing, Drosophila, Edmond Halley, Filter Bubble, Firefox, Google Earth, Howard Rheingold, index card, informal economy, Isaac Newton, Johann Wolfgang von Goethe, knowledge worker, Louis Daguerre, Menlo Park, optical character recognition, RFID, Richard Thaler, Silicon Valley, social graph, software studies, statistical model, Stephen Hawking, Steven Pinker, text mining, time value of money, trade route, Turing machine, urban renewal, Vannevar Bush

The Economic Journal 6, no. 24 (December 1896): 509–534. 13. Ibid., 520, 525, 526. Fisher returned to this subject repeatedly, most notably in The Nature of Capital and Income (New York: Macmillan, 1906). The assumption that money should earn interest when it is lent out is based on the principle modern economists call the time value of money. Historically, this principle derives from very old Christian notions about the relationship between time and God; theorists who wanted to circumvent the Church’s ban on usury elaborated on it in the sixteenth century. One of the economic theorists whose work on this subject Fisher specifically engaged in Appreciation and Interest was Eugene von Bohm-Bawerk, the Austrian finance minister.

The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk by William J. Bernstein

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asset allocation, backtesting, capital asset pricing model, computer age, correlation coefficient, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, fixed income, index arbitrage, index fund, Long Term Capital Management, p-value, passive investing, prediction markets, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, South Sea Bubble, the scientific method, time value of money, transaction costs, Vanguard fund, Yogi Berra, zero-coupon bond

This theory is Odds and Ends 121 advanced by Fama and French in the form of their three-factor model. This simple, yet powerful construct is extraordinarily useful in understanding long-term returns in markets around the globe. Simply put, any stock asset class earns four different returns: ■ The risk-free rate, that is, the time value of money. Usually set at the short-term T-bill rate. ■ The market-risk premium. That additional return earned by exposing yourself to the stock market. ■ The size premium. The additional return earned by owning smallcompany stocks. ■ The value premium. The additional return earned by owning value stocks.


pages: 823 words: 220,581

Debunking Economics - Revised, Expanded and Integrated Edition: The Naked Emperor Dethroned? by Steve Keen

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accounting loophole / creative accounting, banking crisis, banks create money, barriers to entry, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, butterfly effect, capital asset pricing model, cellular automata, central bank independence, citizen journalism, clockwork universe, collective bargaining, complexity theory, correlation coefficient, credit crunch, David Ricardo: comparative advantage, debt deflation, diversification, double entry bookkeeping, en.wikipedia.org, Eugene Fama: efficient market hypothesis, experimental subject, Financial Instability Hypothesis, Fractional reserve banking, full employment, Henri Poincaré, housing crisis, Hyman Minsky, income inequality, invisible hand, iterative process, John von Neumann, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market clearing, market microstructure, means of production, minimum wage unemployment, open economy, place-making, Ponzi scheme, profit maximization, quantitative easing, RAND corporation, random walk, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Schrödinger's Cat, scientific mainstream, seigniorage, six sigma, South Sea Bubble, stochastic process, The Great Moderation, The Wealth of Nations by Adam Smith, Thorstein Veblen, time value of money, total factor productivity, tulip mania, wage slave

Fisher thus has the dubious distinction of fathering both the conventional theory of finance – which, like his 1929 self, reassures finance markets that they are rational – and an unconventional theory which argues that speculative bubbles can cause economic depressions. Pre-Depression Fisher: the time value of money In 1930 Fisher published The Theory of Interest, which asserted that the interest rate ‘expresses a price in the exchange between present and future goods’ (Fisher 1930).3 This argument was a simple extension of the economic theory of prices to the puzzle of how interest rates are set, but it has an even older genealogy: it was first argued by Jeremy Bentham, the true father of modern neoclassical economics, when in 1787 he wrote ‘In defence of usury.’

In the case of the stock market, it means at least four things: that the collective expectations of stock market investors are accurate predictions of the future prospects of companies; that share prices fully reflect all information pertinent to the future prospects of traded companies; that changes in share prices are entirely due to changes in information relevant to future prospects, where that information arrives in an unpredictable and random fashion; and that therefore stock prices ‘follow a random walk,’ so that past movements in prices give no information about what future movements will be – just as past rolls of dice can’t be used to predict what the next roll will be. These propositions are a collage of the assumptions and conclusions of the ‘efficient markets hypothesis’ (EMH) and the ‘capital assets pricing model’ (CAPM), which were formal extensions to Fisher’s (pre-Depression) time value of money theories. Like the Fisher theories of old, these new theories were microeconomic in nature, and presumed that finance markets are continually in equilibrium. There were several economists who developed this sophisticated equilibrium analysis of finance. In what follows I s on the work of W.


pages: 237 words: 72,716

The Inequality Puzzle: European and US Leaders Discuss Rising Income Inequality by Roland Berger, David Grusky, Tobias Raffel, Geoffrey Samuels, Chris Wimer

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Branko Milanovic, Celtic Tiger, collective bargaining, corporate governance, corporate social responsibility, double entry bookkeeping, equal pay for equal work, fear of failure, financial innovation, full employment, Gini coefficient, hiring and firing, illegal immigration, income inequality, invisible hand, labour market flexibility, labour mobility, Long Term Capital Management, microcredit, offshore financial centre, principal–agent problem, profit maximization, rent-seeking, shareholder value, Silicon Valley, Silicon Valley startup, time value of money, very high income

The physical plant of the United States, bridges, ports, airports, our airlines, our railroads, whatever the case may be, is very tough to modernize and re-invest with the level of taxation and the slow return on capital that you get due to the depreciation schedules in our tax code. If you did those two things, it makes the tax shield of interest deductibility less valuable relative to the industrial sector. The only thing that happens if you allow the expensing of capital is, at worst, the government loses the time value of money, and that assumes the investment would have been made to begin with. But in bad times, the reality is most of those investments aren’t made, because every board of directors when business is getting bad has the same refrain, “push off the capital, ” “make do with what you have, ” “don’t spend,” “cash is king.”


pages: 381 words: 101,559

Currency Wars: The Making of the Next Gobal Crisis by James Rickards

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Asian financial crisis, bank run, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Black Swan, borderless world, Bretton Woods, BRICs, British Empire, business climate, capital controls, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, Deng Xiaoping, diversification, diversified portfolio, Fall of the Berlin Wall, family office, financial innovation, floating exchange rates, full employment, game design, German hyperinflation, Gini coefficient, global rebalancing, global reserve currency, high net worth, income inequality, interest rate derivative, Kenneth Rogoff, labour mobility, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, money: store of value / unit of account / medium of exchange, Network effects, New Journalism, Nixon shock, offshore financial centre, oil shock, open economy, paradox of thrift, price mechanism, price stability, private sector deleveraging, quantitative easing, race to the bottom, RAND corporation, rent-seeking, reserve currency, Ronald Reagan, sovereign wealth fund, special drawing rights, special economic zone, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, time value of money, too big to fail, value at risk, War on Poverty, Washington Consensus

Economists called this the price-specie-flow mechanism (also the price-gold-flow mechanism). This rebalancing worked naturally without central bank intervention. It was facilitated by arbitrageurs who would buy “cheap” gold in one country and sell it as “expensive” gold in another country once exchange rates, the time value of money, transportation costs and bullion refining costs were taken into account. It was done in accordance with the rules of the game, which were well-understood customs and practices based on mutual advantage, common sense and the profits of arbitrage. Not every claim had to be settled in gold immediately.

A Primer for the Mathematics of Financial Engineering by Dan Stefanica

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asset allocation, Black-Scholes formula, capital asset pricing model, constrained optimization, delta neutral, discrete time, Emanuel Derman, implied volatility, law of one price, margin call, quantitative trading / quantitative finance, Sharpe ratio, short selling, time value of money, transaction costs, volatility smile, yield curve, zero-coupon bond

An important consequence of the law of one price is the fact that, if the value of a portfolio at time T in the future is independent of the state of the market at that time, then the value of the portfolio in the present is the risk-neutral discounted present value of the portfolio at time T. Before we state this result formally, we must clarify the meaning of "riskneutral discounted present value". This refers to the time value of money: cash can be deposited at time tl to be returned at time t2 (t2 > tl), with interest. The interest rate depends on many factors, one of them being the probability of default of the party receiving the cash deposit. If this probability is zero, or close to zero (the US Treasury is considered virtually impossible to default - more money can be printed to pay back debt, for example), then the return is considered risk-free.


pages: 350 words: 103,270

The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again by Nicholas Dunbar

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asset-backed security, bank run, banking crisis, Basel III, Black Swan, Black-Scholes formula, bonus culture, capital asset pricing model, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delayed gratification, diversification, Edmond Halley, facts on the ground, financial innovation, fixed income, George Akerlof, implied volatility, index fund, interest rate derivative, interest rate swap, Isaac Newton, Kenneth Rogoff, Long Term Capital Management, margin call, market bubble, Nick Leeson, Northern Rock, offshore financial centre, price mechanism, regulatory arbitrage, rent-seeking, Richard Thaler, risk tolerance, risk/return, Ronald Reagan, shareholder value, short selling, statistical model, The Chicago School, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, yield curve

For an excellent high-level account of Bob Diamond’s rise to power at Barclays, see Martin Vander Weyer, Falling Eagle: The Decline of Barclays Bank (London: Weidenfeld, 2000). 4. Usi used this example in an interview for Derivatives Strategy magazine, June 1997. 5. Note that we ignore any mention of time, or the time value of money, in this example, which is the equivalent of setting the risk-free interest rate to zero. 6. One might argue that since the market values the loans at $800 million, the bank ought to write down the value of the equity investment to zero. However, accounting rules for loan books don’t require such recognitions to take place. 7.


pages: 346 words: 102,625

Early Retirement Extreme by Jacob Lund Fisker

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8-hour work day, active transport: walking or cycling, barriers to entry, clean water, Community Supported Agriculture, delayed gratification, discounted cash flows, diversification, don't be evil, dumpster diving, financial independence, game design, index fund, invention of the steam engine, inventory management, loose coupling, market bubble, McMansion, passive income, peak oil, place-making, Ponzi scheme, psychological pricing, the scientific method, time value of money, transaction costs, wage slave, working poor

Economic goals for someone aspiring to be a Renaissance man are to understand the difference between price and value. Value is psychological; price is determined by the market. learn to consider more than the immediate consequences of a choice. Also consider the future consequences--for example, opportunity cost and the time-value of money. Learn to see the unseen. learn to consider more than the consequences of a choice for just one group of people, but for all others as well. realize that economic agents all represent special interests that typically interpret the situation according to their own interests or political views.


pages: 355 words: 92,571

Capitalism: Money, Morals and Markets by John Plender

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Andrei Shleifer, asset-backed security, bank run, Berlin Wall, Big bang: deregulation of the City of London, Black Swan, bonus culture, Bretton Woods, business climate, Capital in the Twenty-First Century by Thomas Piketty, central bank independence, collapse of Lehman Brothers, collective bargaining, computer age, Corn Laws, corporate governance, credit crunch, Credit Default Swap, David Ricardo: comparative advantage, deindustrialization, Deng Xiaoping, discovery of the americas, diversification, Eugene Fama: efficient market hypothesis, eurozone crisis, failed state, Fall of the Berlin Wall, fiat currency, financial innovation, financial intermediation, Fractional reserve banking, full employment, Gordon Gekko, greed is good, Hyman Minsky, income inequality, inflation targeting, invention of the wheel, invisible hand, Isaac Newton, James Watt: steam engine, Johann Wolfgang von Goethe, John Maynard Keynes: Economic Possibilities for our Grandchildren, joint-stock company, Joseph Schumpeter, labour market flexibility, London Interbank Offered Rate, London Whale, Long Term Capital Management, manufacturing employment, Mark Zuckerberg, market bubble, market fundamentalism, means of production, Menlo Park, moral hazard, moveable type in China, Nick Leeson, Northern Rock, Occupy movement, offshore financial centre, paradox of thrift, Plutocrats, plutocrats, price stability, principal–agent problem, profit motive, quantitative easing, railway mania, regulatory arbitrage, Richard Thaler, rising living standards, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Reagan, savings glut, shareholder value, short selling, Silicon Valley, South Sea Bubble, spice trade, Steve Jobs, technology bubble, The Chicago School, The Great Moderation, the map is not the territory, The Wealth of Nations by Adam Smith, Thorstein Veblen, time value of money, too big to fail, tulip mania, Upton Sinclair, We are the 99%, Wolfgang Streeck

Lending was often a form of help to a neighbour in distress. Charging interest could thus be seen as a breach of trust. From a more economic perspective, the bias against charging interest is perfectly logical if you bear in mind the context. The mindset stems not so much from a failure to grasp the time value of money as from the nature of a world where minimal or non-existent growth in per capita income was the norm. As the earlier quotation from Aristotle’s Politics implied, without growth, trade struck people as a zero-sum game where it was felt that one man’s profit could only be earned at the cost of inflicting loss on another man.


pages: 1,797 words: 390,698

Power at Ground Zero: Politics, Money, and the Remaking of Lower Manhattan by Lynne B. Sagalyn

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affirmative action, airport security, Bonfire of the Vanities, clean water, conceptual framework, corporate governance, deindustrialization, Donald Trump, Edward Glaeser, estate planning, Frank Gehry, Guggenheim Bilbao, high net worth, informal economy, intermodal, iterative process, Jane Jacobs, mortgage debt, New Urbanism, place-making, rent control, Rosa Parks, Silicon Valley, sovereign wealth fund, the built environment, the High Line, time value of money, too big to fail, Torches of Freedom, urban decay, urban planning, urban renewal, white flight, young professional

In addition to this basic structure, the agency outlined other ways in which it could provide additional support, including rent abatements meant to ensure the phased advancement of all three office buildings while protecting “within reason” the Port Authority’s further exposure to risk. For the Port Authority, the financial implications of the proposal depended upon the lease-up rate of Tower 4, but the downside estimate of its exposure was $1.4 billion (on a net present value basis accounting for the time value of money) if SPI failed completely and the agency lost its ground rent and was forced to absorb the full cost of the infrastructure buildout necessary for the site’s operation. If SPI accepted the Port Authority’s proposal, its losses would range anywhere from $280 million to $1 billion, depending on how quickly Silverstein could lease Tower 4.

His wear-you-down technique in strung-out negotiations seemed to be having an effect. City and state officials were frustrated; they thought Tower 4 issues had been settled. Everyone was exhausted. Port Authority officials argued that the agency would lose at least $100 million (adjusted for the time value of money) over the term of the ground lease if it gave into the proposal Silverstein was now making to lower rent payments on Tower 4. They held firm to their positon. In the process of resolving this last item, however, the state, wanting to see a deal done, gave up half of its potential profit participation in Tower 3, which would only generate a return in the event of a capital transaction triggered by SPI.38 Finally, the parties were in agreement on the funding of development costs, the details of debt financing and credit support, and other related financial items.39 The last major negotiation involved the “Construction Partnership” between the PA and SPI.

(It was the same with the Condé Nast transaction.) Presentation of “select terms of the lease” as described in a bare two pages of the minutes of the board meeting was high level, economically light. The oft-cited revenue intake of $875 million over the life of the fifteen-year lease was in nominal dollars, unadjusted for the time value of money. The day before the transaction went before the board of commissioners, Governors Cuomo and Christie issued a joint statement announcing the selection of Legends and called on the board to approve the agreement. In the lease with Legends, now available online through a FOI request, the rent payment arrangements as well as any other specifics on the economics of the transaction were redacted.76 Ironically, as Brown pointed out, there is far more financial information publicly available for many privately owned towers than there is for 1 World Trade.


pages: 423 words: 149,033

The fortune at the bottom of the pyramid by C. K. Prahalad

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barriers to entry, business process, call centre, cashless society, clean water, collective bargaining, corporate social responsibility, deskilling, disintermediation, farmers can use mobile phones to check market prices, financial intermediation, Hernando de Soto, hiring and firing, income inequality, late fees, Mahatma Gandhi, market fragmentation, microcredit, new economy, profit motive, purchasing power parity, rent-seeking, shareholder value, The Fortune at the Bottom of the Pyramid, time value of money, transaction costs, working poor

The process is so opaque to the farmer that the broker and the officials have opportunities to be arbitrary about the quality of the title and the value of the land. More important, they have the ability to decide how long the process will take. They can give this particular case the level of priority that they think is appropriate. Corruption is about providing privileged access to resources and recognizing the time value of money. Corruption is a market mechanism for privileged access. Bureaucrats use microregulations to control access, transparency, and therefore time. TGC is about eliminating the opaqueness in the system and providing ease of access. Changing laws and regulations does not help the ordinary citizen if the system is not transparent or if access is not easy.


pages: 402 words: 110,972

Nerds on Wall Street: Math, Machines and Wired Markets by David J. Leinweber

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AI winter, algorithmic trading, asset allocation, banking crisis, barriers to entry, Big bang: deregulation of the City of London, butterfly effect, buttonwood tree, buy low sell high, capital asset pricing model, citizen journalism, collateralized debt obligation, corporate governance, Craig Reynolds: boids flock, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Danny Hillis, demand response, disintermediation, distributed generation, diversification, diversified portfolio, Emanuel Derman, en.wikipedia.org, experimental economics, financial innovation, Gordon Gekko, implied volatility, index arbitrage, index fund, information retrieval, Internet Archive, John Nash: game theory, Khan Academy, load shedding, Long Term Capital Management, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, market fragmentation, market microstructure, Mars Rover, moral hazard, mutually assured destruction, natural language processing, Network effects, optical character recognition, paper trading, passive investing, pez dispenser, phenotype, prediction markets, quantitative hedge fund, quantitative trading / quantitative finance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Renaissance Technologies, Richard Stallman, risk tolerance, risk-adjusted returns, risk/return, Ronald Reagan, semantic web, Sharpe ratio, short selling, Silicon Valley, Small Order Execution System, smart grid, smart meter, social web, South Sea Bubble, statistical arbitrage, statistical model, Steve Jobs, Steven Levy, Tacoma Narrows Bridge, the scientific method, The Wisdom of Crowds, time value of money, too big to fail, transaction costs, Turing machine, Upton Sinclair, value at risk, Vernor Vinge, yield curve, Yogi Berra

Citadel’s Matt Andresen and other attendees considered the opportunity to move over-the-counter (OTC)-traded CDSs onto electronic exchanges as the single best product opportunity in many years—a high standard, given the electronic transformation of markets in the recent past.”9 The mandates of federal regulation, combined with a highoctane mix of the standard Wall Street motivators of fear and greed, give us hope that this element of the technology solution will happen quickly. Stupid Engineering Tricks Engineers have had some great ideas. History’s greatest technological advances are often cited as fire, the wheel, and storing instructions as data. The first is arguably a discovery, but the others are inventions. We can add a few more—the time value of money, the automobile, the transistor, and the World Wide Web. In the Introduction, the structure of Mutually Assured Survival (dreadfully mislabeled as Mutually Assured Destruction) was given high marks. Not all military technology ideas had similar merit. In Imaginary Weapons: A Journey Through the Pentagon’s Scientific Underworld, Defense Technology International editor Sharon Weinberger tells the remarkable story of how tens of millions of dollars were spent on a crackpot idea for what amounted to a nuclear hand grenade, despite the efforts of the most senior Pentagon scientists to scuttle the project, and the dubious utility of such a weapon.


pages: 289 words: 113,211

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

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affirmative action, Albert Einstein, asset allocation, backtesting, Black Swan, Black-Scholes formula, Bonfire of the Vanities, butterfly effect, commodity trading advisor, computer age, disintermediation, diversification, double entry bookkeeping, Edward Lorenz: Chaos theory, family office, financial innovation, fixed income, frictionless, frictionless market, George Akerlof, implied volatility, index arbitrage, Jeff Bezos, London Interbank Offered Rate, Long Term Capital Management, loose coupling, margin call, market bubble, market design, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, new economy, Nick Leeson, oil shock, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk/return, Robert Shiller, Robert Shiller, rolodex, Saturday Night Live, shareholder value, short selling, Silicon Valley, statistical arbitrage, The Market for Lemons, time value of money, too big to fail, transaction costs, tulip mania, uranium enrichment, yield curve, zero-coupon bond

The typical product that Goldstein’s group sold after he had his group up and ready to trade in 1992 gave the investor the upside of the index like the FTSE Index (the market index in the United Kingdom) at the end of five years, and guaranteed that if the FTSE fell the investors would at a minimum get their money back. Of course, even the return of the principal implied a loss given the time value of money—if the funds had been invested over that period they would have ended up with more than their initial investment—but nonetheless it was very attractive: At the best you make money with the equity market and at the worst you end up with your money back. Goldstein also offered long-dated options on individual stocks.


pages: 444 words: 151,136

Endless Money: The Moral Hazards of Socialism by William Baker, Addison Wiggin

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Andy Kessler, asset allocation, backtesting, bank run, banking crisis, Berlin Wall, Bernie Madoff, Black Swan, Branko Milanovic, Bretton Woods, BRICs, business climate, capital asset pricing model, corporate governance, correlation does not imply causation, credit crunch, Credit Default Swap, crony capitalism, cuban missile crisis, currency manipulation / currency intervention, debt deflation, Elliott wave, en.wikipedia.org, Fall of the Berlin Wall, feminist movement, fiat currency, fixed income, floating exchange rates, Fractional reserve banking, full employment, German hyperinflation, housing crisis, income inequality, index fund, inflation targeting, Joseph Schumpeter, laissez-faire capitalism, land reform, liquidity trap, Long Term Capital Management, McMansion, moral hazard, mortgage tax deduction, naked short selling, offshore financial centre, Ponzi scheme, price stability, pushing on a string, quantitative easing, RAND corporation, rent control, reserve currency, riskless arbitrage, Ronald Reagan, school vouchers, seigniorage, short selling, Silicon Valley, six sigma, statistical arbitrage, statistical model, Steve Jobs, The Great Moderation, the scientific method, time value of money, too big to fail, upwardly mobile, War on Poverty, Yogi Berra, young professional

Noble in 1816).2 By the 19th century it was generally accepted that banks could continuously pyramid loans against deposits, making fractional reserve banking the principle mechanism by which money could be created in the economy. Some point out that systems of circulating receipts for physical goods constituted paper money well before this time. In the medieval era families such as the Riccis and the Medicis extended credit to customers and accepted an additional fee for the time value of money, but the paper this created was not expanded beyond the value of goods sold. Such credit was non-inflationary, and it also benefitted commerce through the substitution of a less bulky medium of exchange.3 The Gold Standard What in fact is the classical notion of a gold standard, and how well did we adhere to that ideal?


pages: 504 words: 139,137

Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined by Lasse Heje Pedersen

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algorithmic trading, Andrei Shleifer, asset allocation, backtesting, bank run, banking crisis, barriers to entry, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, commodity trading advisor, conceptual framework, corporate governance, credit crunch, Credit Default Swap, currency peg, David Ricardo: comparative advantage, declining real wages, discounted cash flows, diversification, diversified portfolio, Emanuel Derman, equity premium, Eugene Fama: efficient market hypothesis, fixed income, Flash crash, floating exchange rates, frictionless, frictionless market, Gordon Gekko, implied volatility, index arbitrage, index fund, interest rate swap, late capitalism, law of one price, Long Term Capital Management, margin call, market clearing, market design, market friction, merger arbitrage, mortgage debt, New Journalism, paper trading, passive investing, price discovery process, price stability, purchasing power parity, quantitative easing, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, systematic trading, technology bubble, time value of money, total factor productivity, transaction costs, value at risk, Vanguard fund, yield curve, zero-coupon bond

We will refer to these free cash flows as the “dividends” Dt, but they should be interpreted broadly as all cash returned to shareholders (including capital returned through share repurchases), less the capital that needs to be injected by shareholders (through seasoned equity offerings). Of course, we cannot just add up dividends across different time periods because we must account for the time value of money and the uncertainty of the future cash flows. We start by considering how the value today depends on what happens over the next time period, say the next year. Today’s intrinsic value depends on the next dividend Dt+1, the value next period, and the required rate of return kt (also called the discount rate) over this time period.


pages: 537 words: 144,318

The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money by Steven Drobny

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Albert Einstein, Asian financial crisis, asset allocation, asset-backed security, backtesting, banking crisis, Bernie Madoff, Black Swan, Bretton Woods, BRICs, British Empire, business process, capital asset pricing model, capital controls, central bank independence, collateralized debt obligation, Commodity Super-Cycle, commodity trading advisor, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, debt deflation, diversification, diversified portfolio, equity premium, family office, fiat currency, fixed income, follow your passion, full employment, Hyman Minsky, implied volatility, index fund, inflation targeting, interest rate swap, inventory management, invisible hand, London Interbank Offered Rate, Long Term Capital Management, market bubble, market fundamentalism, market microstructure, moral hazard, North Sea oil, open economy, peak oil, pension reform, Ponzi scheme, prediction markets, price discovery process, price stability, private sector deleveraging, profit motive, purchasing power parity, quantitative easing, random walk, reserve currency, risk tolerance, risk-adjusted returns, risk/return, savings glut, Sharpe ratio, short selling, sovereign wealth fund, special drawing rights, statistical arbitrage, stochastic volatility, The Great Moderation, time value of money, too big to fail, transaction costs, unbiased observer, value at risk, Vanguard fund, yield curve

Anecdotally, as a sanity check, the consensus amongst the Turkish political and corporate leaders we met on the trip was orthogonal to the consensus in London and New York. With one-year yields above 100 percent, there was a lot of potential alpha in the trade and you had a massive cushion. Turkey is a very large economy where the population has understood the time value of money since Ottoman rule. The country has never had capital controls. Financially speaking, the Turkish population today is much more sophisticated than that of the United States, the United Kingdom, or even Switzerland. Persistent high inflation has forced the merchant class to develop a certain financial knowledge; cab drivers wax lyrically about simple and compounded yield, and the average bank managers are familiar with Treasury funding and supply schedules.


pages: 819 words: 181,185

Derivatives Markets by David Goldenberg

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Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Norbert Wiener, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, Y2K, yield curve, zero-coupon bond

What would be the value of your combined position at time T (long the forward at time t and short the same forward at time t′)? 84 FORWARD CONTRACTS AND FUTURES CONTRACTS h. Ignoring discounting, what would be the value of your combined position at time t′? i. Should we discount g. to get h.? That is, should we account for the time value of money to transform the value in g. to the value in h.? Hint: What is your investment in the long position initiated at time t? What is your investment in the short position initiated at time t′? We discount in order to take into account the opportunity cost of an investment. What is the opportunity cost of your combined position?


pages: 1,073 words: 302,361

Money and Power: How Goldman Sachs Came to Rule the World by William D. Cohan

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asset-backed security, Bernie Madoff, buttonwood tree, collateralized debt obligation, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversified portfolio, fear of failure, financial innovation, fixed income, Ford paid five dollars a day, Goldman Sachs: Vampire Squid, Gordon Gekko, high net worth, hiring and firing, hive mind, Hyman Minsky, interest rate swap, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, merger arbitrage, moral hazard, mortgage debt, paper trading, passive investing, Ponzi scheme, price stability, profit maximization, risk tolerance, Ronald Reagan, Saturday Night Live, South Sea Bubble, time value of money, too big to fail, traveling salesman, value at risk, yield curve, Yogi Berra

Since rates on loans from commercial banks were high, one means New York’s small merchants had of obtaining cash was to sell their promissory notes or commercial paper to men like Marcus at a discount.” In his telling, Birmingham likened the “commercial paper” of the day—unsecured short-term debts—to a postdated check that could only be cashed six months in the future. Based on prevailing interest rates and the “time value” of money concept—the idea that one dollar in hand today is worth more than one dollar in hand six months from now, because presumably you could invest the money in the interim and earn a return on it—investors such as Marcus Goldman would buy the IOU for cash at a discount today knowing that, all things being equal, over time he could get face value for the paper.


pages: 892 words: 91,000

Valuation: Measuring and Managing the Value of Companies by Tim Koller, McKinsey, Company Inc., Marc Goedhart, David Wessels, Barbara Schwimmer, Franziska Manoury

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air freight, barriers to entry, Basel III, BRICs, business climate, business process, capital asset pricing model, capital controls, cloud computing, compound rate of return, conceptual framework, corporate governance, corporate social responsibility, credit crunch, Credit Default Swap, discounted cash flows, distributed generation, diversified portfolio, energy security, equity premium, index fund, iterative process, Long Term Capital Management, market bubble, market friction, meta analysis, meta-analysis, new economy, p-value, performance metric, Ponzi scheme, price anchoring, purchasing power parity, quantitative easing, risk/return, Robert Shiller, Robert Shiller, shareholder value, six sigma, sovereign wealth fund, speech recognition, technology bubble, time value of money, too big to fail, transaction costs, transfer pricing, value at risk, yield curve, zero-coupon bond

2 Fundamental Principles of Value Creation Companies create value for their owners by investing cash now to generate more cash in the future. The amount of value they create is the difference between cash inflows and the cost of the investments made, adjusted to reflect the fact that tomorrow’s cash flows are worth less than today’s because of the time value of money and the riskiness of future cash flows. As we will demonstrate, a company’s return on invested capital (ROIC)1 and its revenue growth together determine how revenues are converted to cash flows (and earnings). That means the amount of value a company creates is governed ultimately by its ROIC, revenue growth, and ability to sustain both over time.