# time value of money

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Risk Management in Trading by Davis Edwards

The time that has passed 74 RISK MANAGEMENT IN TRADING 0.1% 0.2% 50/50 chance of +1 or −1 Cumulative Result 10 9 8 7 6 5 4 3 2 1 0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 1.0% 0.4% 1.8% 0.8% 1.6% 3.1% 25.0% 50.0% 100.0% 15.6% 25.0% 37.5% 37.5% 25.0% 16.4% 21.9% 23.4% 6.3% 24.6% 27.3% 15.6% 16.4% 20.5% 16.4% 11.7% 10.9% 9.4% 3.1% 24.6% 27.3% 31.3% 25.0% 12.5% 20.5% 24.6% 27.3% 31.3% 11.7% 16.4% 21.9% 23.4% 31.3% 37.5% 50.0% 50.0% 4.4% 7.0% 10.9% 9.4% 6.3% 12.5% 3.1% 5.5% 7.0% 5.5% 3.1% 1.6% 0.8% 4.4% 1.8% 1.0% 0.4% 0.2% 0.1% 0 1 2 3 4 5 6 7 8 9 10 Time FIGURE 3.9 Dispersion in a Random Series For financial mathematics, the Wiener process is often generalized to include a constant drift term that pushes prices upward. The constant drift term is due to risk‐free inflation (and described later in the chapter in the “time value of money” discussion). Continuous time versions of this process are called Generalized Wiener Process or the Ito Process. (See Equation 3.8, A Stochastic Process.) A stochastic process with discrete time steps can be described as: ΔSt = μΔt + σΔWt St or ΔSt = μSt Δt + σSt ΔWt where ΔSt Change in Price. The change in price that will occur St Price. The price of an asset at time t (3.8) Financial Mathematics μ Drift.

For example, if the variables are highly correlated, then it is necessary to consider the second‐order and cross‐relationship factors. For example, models of stochastic price processes commonly need additional terms to be considered. (See Equation 3.20, Generalized Taylor Series on Two Factors.) Finding f(x + Δx, y + Δy) for a function f(x, y): df = ⎤ df df d2 f d2 f 1 ⎡ d2 f Δx + Δy + ⎢ 2 (Δx)2 + 2 (Δy)2 + 2 ΔxΔy ⎥ (3.20) dx dy dxdy 2 ⎣ dx dy ⎦ TIME VALUE OF MONEY Financial mathematics tends to base all of its calculations on the concept of money. However, they value of money is not constant. For example, a dollar in 2014 does not purchase the same amount of goods or services that the same dollar would have purchased in 1914. When looking at the value of money in the future, an adjustment has to be made to the value. 91 Financial Mathematics Additionally, even when ignoring inflation, a dollar on hand is worth more than the promise of a dollar in the future.

For example, a trading system might identify simultaneous purchases and sales in the same asset (wash trades) that are often an indicator of market manipulation. ■ ■ ■ ■ ■ TEST YOUR KNOWLEDGE 1. Sharpe Ratios and Information Ratios both measure what? A. The ease of liquidating trades B. Expected excess returns divided by volatility (standard deviation of returns) C. The theoretical price of the asset if held to maturity based on commonly accepted financial assumptions like non-existence of arbitrage and time value of money. D. The maximum expected drawdown of a trading strategy 2. What is the primary benefit of out-of-sample backtesting? A. It allows the strategy to be modeled with normally distributed returns. B. It decreases volatility of the strategy. Backtesting and Trade Forensics 3. 4. 5. 6. 7. 119 C. It increases the expected returns of the strategy. D. It reduces the likelihood of over-fitting a model.

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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

Investopedia explains Tier 1 Capital Equity capital includes instruments that cannot be redeemed at the discretion of the holder. 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. Because of this, the sooner it starts earning interest, the better. For example, assuming a 5% interest rate, a \$100 investment today will be worth \$105 in one year (\$100 multiplied by 1.05).

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. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).

Related Terms: • Ask • Market Maker • New York Stock Exchange—NYSE • Bid • Pink Sheets Black Scholes Model What Does Black Scholes Model Mean? 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

Make sure you understand the difference between various types of property ownership: individual ownership, joint tenancy, and tenancy by the entirety, as each has a different effect on what happens to that property upon your death. 5. 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. In fact, if you are in the business world, owning a financial calculator is a necessary tool in order for you to succeed.

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. Starting early and having a better appreciation of your most valuable asset—time— will give you a tremendous advantage to achieving your financial goals.

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

In any event, he likely tutored others in mathematics, the laws of probability, and in finance, and the London beaux who frequented the gambling tables undoubtedly considered his consulting services valuable. 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. He showed that annuity buyers at most age groups were, in effect, getting a price subsidy for purchasing financial security over their lives.

He invested in institutional bakeries that supplied the temple. 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. Without the ability to shift money through time—to borrow against future income—Dumuzi-gamil might not have been able to set up shop.

The system was widely used for commercial disputes, many involving the Athenian grain trade. 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. What risk did this economic cooperation represent? Why did it merit the death penalty?

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

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.

The way in which money changes its value in time is a complex issue of fundamental importance in ﬁnance. 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. To begin with, we shall consider the case when interest is attracted only by the principal, which remains unchanged during the period of investment.

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

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. Risk premium A rational investor, if given the choice between investing in a bank or bond promising to pay 5% interest a year and a project to build a series of holiday homes on Mars, which also promises to pay 5%, would probably prefer to invest in a bank.

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. The result is called the net present value or npv. 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”.

The Trade Lifecycle: Behind the Scenes of the Trading Process (The Wiley Finance Series) by Robert P. Baker

Money can be borrowed for different periods of time (known as term) and the major set of financial products in interest rates are divided into three terms short term (less than one year) are known as cash or money market trades medium term (usually from one to two years) are futures longer term (two or more years) are swaps. Interest and the time value of money Interest is paid to attract lenders to part with money which they could otherwise have used for purchasing other assets or kept for security. A person making a loan to 33 34 THE TRADE LIFECYCLE someone else will therefore charge interest to compensate for the loss of opportunity to use his own money and because there is a reduction in his liquidity meaning that he has less ability to cope with sudden demands on his money such as to pay wages or fix broken machinery. The result of charging interest when money is loaned causes an effect known as the ‘the time value of money’. In essence this effect means that money in the future is worth less than money now. This is not to be confused with inflation which is caused by price rises.

Since products in all asset classes require discounting of their future cashflows, we see the importance of the discount curve and hence interest rate products to the whole of financial trading. Interest rates are therefore a fundamental asset class used by all other asset classes. Removing credit effects The aim of building a discount curve is to quantify the time value of money. Whenever two counterparties engage in a deal they have to take into account the risk of default and will charge a premium to mitigate this risk; the greater the chance of default, the higher the risk. This credit effect distorts the price of the product which could be a deposit or swap used in building the discount curve and hence the discount curve is altered and no longer reflects purely the time value of money. An alternative instrument which is better at removing the effect of credit is the Overnight Indexed Swap (OIS). This is a swap in which one party pays fixed and the other pays the geometrical average of all overnight interest rates in the period of the swap.

The discount curve As well as being important in their own right, the class of interest rate products is vital for construction of the discount curve. We saw in the previous chapter that most trades give rise to cashflows in the future. If we are going to assess the worth of future cashflows we cannot take them at face value. Those due sooner are worth more than those due later because of the time value of money. Therefore we need a means to weight future cashflows according to their depreciation over time. This can be done in many ways; one of the most common is to construct a discount curve. The discount curve determines the rate at which the value of money decreases over time. It is constructed by taking an active (liquid) set of interest rate products – deposits, futures and swaps – and using their prices to imply a set of factors at future time periods known as discount factors.

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

Because sentimental value is nil, the fundamental determinants of stock values are dividends, their expected growth rates, and interest rates. Period. 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.

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?) Furthermore, perhaps even more so than with shares of the Green Bay Packers, genuine nonmonetary benefits may accompany homeownership. A house is, after all, something personal—you live in it. It may be worth more to you than the rent you save each month.

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. That’s it.

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

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. A million dollars, invested at a Compounding (discussed next) interest rate of 5 percent, will be \$1,276,281.56 five years from now. Why give up the extra quarter of a million dollars if you don’t need to? 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. What’s the maximum amount you should be willing to pay for it today? Assuming your Next Best Alternative is another risk-free investment with a 5 percent interest rate, you shouldn’t pay anything more than \$952,380. Why? 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. If you pay less than that amount, you’ll come out ahead as long as your assumptions are correct. (Note: this is the “discounted cash flow method” we discussed in the Four Pricing Methods.) The Time Value of Money is an extremely versatile concept, and a full exploration is beyond the scope of this book. For a more in-depth examination, I recommend picking up The McGraw-Hill 36-Hour Course in Finance for Nonfinancial Managers by Robert A.

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

EXHIBIT 3.23(a) Implied Exit Multiple (End-of-Year Discounting) EXHIBIT 3.23(b) Implied Exit Multiple (Mid-Year Discounting, see Exhibit 3.26) STEP V. 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. The discount factor is the fractional value representing the present value of one dollar received at a future date given an assumed discount rate.

EXHIBIT 4.5 IRR Timeline Example Returns Analysis - Cash Return In addition to IRR, sponsors also examine returns on the basis of a multiple of their cash investment (“cash return”). 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).

Returns at Various Exit Years In Exhibit 5.41, we calculated IRR and cash return assuming an exit at the end of each year in the projection period using the fixed 7.5x EBITDA exit multiple. 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). EXHIBIT 5.41 Returns at Various Exit Years As shown in Exhibit 5.42, for the ValueCo LBO, we assumed a fixed leverage level of 5.1x LTM 9/30/08 EBITDA of \$146.7 million and a 2013E exit year, while sensitizing entry and exit multiples.

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

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.

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Python for Finance by Yuxing Yan

If the revenue is assumed to be distributed evenly within a year, the payback period of this project will be 2.8 years, as shown in the following code: >>>40/50+2 2.8 The payback rule is that if the estimated payback period of our project is less than a critical value (Tcritical), we accept the project. 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. Otherwise, we reject it, as shown in the following conditions:  If IRR ( project ) > Rcapital accept   If IRR ( project ) < Rcapital reject (17) The Python code to estimate an IRR is as follows: def IRR_f(cashflows,interations=100): rate=1.0 investment=cashflows[0] for i in range(1,interations+1): rate*=(1-npv_f(rate,cashflows)/investment) return rate At this stage, this program is quite complex.

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.

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How to Kick Ass on Wall Street by Andy Kessler

* * * And what can you expect to learn from your mentor? 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. It’s not easy and it’s not obvious and chances are if you ask a random person about it they will look at you with a blank stare and tell you to leave them alone.

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The Scandal of Money by George Gilder

Interest rates, for example, register the average expected returns across the economy. With a near-zero-interest-rate policy, the Fed falsely zeroes out the cost of time. This deception retards economic growth. Rather than creating new assets, low-cost money borrowed from tomorrow bids up existing assets today. It brings about no new learning and value, but merely destroys information by distorting the time value of money. Charles Gave of Gavekal explains: “When the bust arrives, assets return to their original values, while debt remains elevated . . . the stock of capital shrinks . . . and real growth slows.”7 In the name of managing money, the Fed is trying to manipulate investors’ time—their sense of present and future valuations. But time is not truly manipulable. It is an irreversible force impinging on every financial decision we make.

It is rearview-mirror monetary policy reflecting the need of recumbent sectors for protection against more-creative domestic and foreign rivals. By seeking to impart a bias of inflation to prices, the commodity basket tends to a zero-sum vision that fosters trade wars of devaluation. The basket of commodities is the one part of the economy that operates as a zero-sum game. As it erodes through the advance of innovation, its prices tend to drift upward, skewing the time value of money. The redemptive force of gold is its neutrality in time and thus its orientation toward the future. Hayeks would substitute an anachronistic commodity basket for a predictable deflation based on the scarcity of time and abundance of learning. Commodities are by definition low entropy, but if all valuation and arbitrage is based on them, politics will converge on the basket and its composition.

Intuitively, different time requirements make a horse more valuable than an apple, a pair of shoes more valuable than a coconut. As the common element in all goods and services, time determines the possibilities for exchange. As a barter economy becomes a commercial economy, these common time factors become manifested in money. The tie between money and time is obvious in the case of loans and savings governed by the “time value of money,” reflected by interest rates. These central capitalist functions still arouse anger and confusion. The French moralist Thomas Piketty sums them up as the exactions of “capital” and the bounties of the “rentier.”4 Dismissing the linkage of time and money as optional and even reprehensible, Piketty follows in the footsteps of philosophers and kings, priests and scholars who for millennia have ruminated restively on the morality and legitimacy of interest payments.

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Warren Buffett Accounting Book: Reading Financial Statements for Value Investing (Warren Buffett's 3 Favorite Books) by Stig Brodersen, Preston Pysh

Let me demonstrate what I’m talking about. Let’s say we are interested in buying a company called XYZ. We believe that company XYZ is going to produce \$100 of cash flow (or profit) over the next ten years. Therefore, at the end of ten years, you’ll have \$100 of cash in your hand. Now, what would you be willing to pay today for that \$100, ten years from now? In order to solve that generic question, let’s start with a basic time-value of money equation. PV = present value or intrinsic value today FV = future value i = discount rate n = number of years Let’s first solve the equation for the PV (or intrinsic value): Now that we have our equation ready, let’s demonstrate how the intrinsic value of company XYZ changes with the two different discount rates (3% and 50%). We will start with 3%. So here’s what that means: if you could buy company XYZ for \$74.41 today, you’ll earn a 3% return annually for the next ten years.

Considering a federal bond is providing a 3% return, you might determine the extra return from company XYZ is not worth the risk. Others might disagree. More importantly, there might be other investment opportunities that could produce a larger return with less risk. These decisions are the definition of opportunity cost. This is what the discount rate is all about. At the start of this section, you’ll remember the questions I asked my children about the time value of money. At a certain point in time, my children, unknowingly, discounted the future cash flow at a rate that made them choose the present dollar over the future dollars. Smart investors understand this process like the backs of their hands. As we move into the next section, you’ll find the calculation for intrinsic value has more parts. The example in this section was to provide a foundation for what a discount rate is and how it’s used to compare opportunity costs.

If they are not, you can’t expect the book value to grow like it did in the past. Your calculations will be inaccurate and misleading. If current and forecasted earnings are consistent with past earnings, they should provide a reasonable expectation of future book value growth; for example, if the company’s current book value is \$10 a share, and we expect the book value growth rate to be 7% based on historical trends, then we would use the simple time-value-of-money formula to estimate the future book value ten years from now: FBV = Future book value = ? PBV = Present book value = \$10 g = Expected growth rate of book value = .07 or 7% n = Number of years into the future = 10 FBV = PBV (1+ g)n FBV = \$10 (1.07) 10 FBV = \$19.67 In an effort to simplify our bond market price formula for stocks, we’ll rename our variables as follows: Annual coupon = The average annual dividend expected over the next n years Therefore C = D Par value = The expected future book value Therefore M = FBV = PBV (1+ g)n Now that we have adjusted the variables, let’s substitute them into the bond equation to arrive at our intrinsic value formula.

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The Latte Factor: Why You Don't Have to Be Rich to Live Rich by David Bach, John David Mann

So if all goes as planned, by the time you read this, I will be living in Florence, eating pasta, drinking wine, and loving my daily gelato with my boys and wife—and writing another book, this one a memoir about my radical sabbatical. Just like Zoey. I might even blog about it and podcast from there. You can join us on the journey at www.davidbach.com. You’ve included some great charts and worksheets here; any additional thoughts on how to use them? The first thing you’ll see are some of my favorite charts that highlight the miracle of compound interest. The first chart, “The Time Value of Money,” motivated me to start saving in my early twenties. Then, I’ve included a chart that shows interest rates varying from 2 through 12 percent (see page 137), so you can see the difference these returns make in how fast your money can potentially grow. Finally, there is a chart that blew my mind when I first saw it in my early twenties, that shows the annualized return of investments dating back to 1926 (see page 138).

There’s a Latte Factor podcast on our website that is a continuation of this interview, which you can listen to for more great ideas. We also have a newsletter I write when I feel inspired; it’s my way of staying in touch with my readers. It’s free, and we don’t do the usual spammy thing and bug you with stuff to buy (until I put out a new book, of course *smile*). Now, go put this little book to work in your life. No regrets! Appendix: Charts * * * THE TIME VALUE OF MONEY START EARLY THE EARLIER YOU START, THE BIGGER YOUR NEST EGG (Assumes 10% Annual Rate of Return) Daily Investment Monthly Investment 10 Years 20 Years 30 Years 40 Years 50 Years \$5 \$150 \$30,727 \$113,905 \$339,073 \$948,612 \$2,598,659 \$10 \$300 \$61,453 \$227,811 \$678,146 \$1,897,224 \$5,197,317 \$15 \$450 \$92,180 \$341,716 \$1,017,220 \$2,845,836 \$7,795,976 \$20 \$600 \$122,907 \$455,621 \$1,356,293 \$3,794,448 \$10,394,634 \$30 \$900 \$184,360 \$683,432 \$2,034,439 \$5,691,672 \$15,591,952 \$40 \$1,200 \$245,814 \$911,243 \$2,712,586 \$7,588,895 \$20,789,269 \$50 \$1,500 \$307,267 \$1,139,053 \$3,390,732 \$9,486,119 \$25,986,586 A PACK A DAY KEEPS RETIREMENT AWAY (Assumes 10% Annual Rate of Return) A Pack a Day Costs Over a Month That Comes to 10 Years 20 Years 30 Years 40 Years 50 Years \$7 \$210 \$43,017 \$159,467 \$474,702 \$1,328,057 \$3,638,122 BOTTLED WATER IS A FORTUNE DOWN THE DRAIN (Assumes 10% Annual Rate of Return) Avg.

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The Investment Checklist: The Art of In-Depth Research by Michael Shearn

Let Your Guard Down. Why Patents, Trademarks, and Other Intellectual Property Protections are Bad for Business.” Inc., August 2006, pp. 109–111. 12. Blackboard 2009 10-K. 13. American Apparel and Footwear Association. ShoeStats, 2008. Accessed May 11, 2011. http://www.apparelandfootwear.org. 14. Wubbe, Eileen. “TSL Profile.” Secured Lender, September 2010, pp. 39. 15. 2004 Four Seasons Annual Report and Time Value of Money, LP interviews with Four Seasons management. 16. Standard & Poor’s Capital IQ. 17. Ibid. 18. Ibid. 19. Steinberg, Richard M. “Merrill Lynch Failed at ERM, and Then Just Failed.” Compliance Week, August 2009, pp. 42–43. 20. Verschoor, Curtis C. “Who Should Be Blamed the Most for the Subprime Loan Scandal?” Strategic Finance, December 2007, pp. 11–12. 21. Tobin, Edward. “Cola Wars Soldiers March Toward Marketing Battle.”

Many analysts were concerned about the drop and believed it was due to deteriorating business conditions, when in fact, it was dropping because of the excess cash on the balance sheet. By removing excess cash, you will understand the ROIC being generated by the operations of the business. This is often referred to as the return on operational capital. In the case of 99 Cent Only Stores, the ROIC excluding cash was much higher than the ROIC including cash, as shown in Table 5.3. Table 5.3 99 Cent Only Stores Return on Invested Capital (ROIC) Source: Time Value of Money, LP internal research and Standard & Poor’s Capital IQ. Include Property, Plant, and Equipment Costs You must include the purchase of fixed assets necessary to operate the business, such as real estate, plant, and equipment. You need to determine whether to use the gross book value of these assets or the depreciated, net book value of these assets: Gross book value takes the historical or acquisition cost of assets without deducting accumulated depreciation or amortization.

Wall Street Journal, October 15, 2003. 55. Edgecliffe-Johnson, Andrew. “The Biggest Beat of Non-fiction Television Eyes a Global Prize.” Financial Times, January 10, 2011. 56. Ignatius, “Mistakes.” 57. Jones, Steven D. “In the Money: Hurd’s H-P Grew, But Charges Pruned Earnings.” Dow Jones News Service, August 10, 2010. 58. “The Brain Behind Teledyne: A Great American Capitalist.” New York Observer, April 7, 2003. 59. Time Value of Money, LP free cash flow estimate. 60. Standard & Poor’s Capital IQ. 61. Western Union 10K reports, 2007 to 2009. 62. Standard & Poor’s Capital IQ and AutoZone 10-K reports, 2002 to 2010. 63. General Motors 10-K reports, 1985 to 1995. 64. Microsoft 10-K reports, 2009 to 2010. CHAPTER 9 Assessing the Quality of Management—Positive and Negative Traits In Chapter 8, we looked at how management operates the business; this chapter shows you how to evaluate the positive and negative traits of the managers themselves.

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

To take the money forward to time ti, the end of the deposit period, we go long bonds maturing at time ti with yield ri and thus multiply the sum by (1 + rr)''. 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. We can quantify precisely how much less by using risk-free bonds. A zero-coupon bond with principal £1 maturing in a year is precisely the same as receiving the sum of £1 in a year.

It is generally easier, though sometimes misleading, to think in terms of interest rates. 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. In these formulas, it is important to realize that r and T are not as independent as they look: r is the yield of a bond which matures at time T, and bonds of different maturities may have different yields.

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Paper Promises by Philip Coggan

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. In addition, the effective burden of repaying the loan capital will be reduced by inflation.

But a system based on regular payments was suited to an industrial age where workers received regular income. 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. On those occasions when they did default, buyers had usually made several payments, ensuring any loss was limited.

Clarida to the Federal Reserve Bank Conference, 21 October 2010. 15 For up-to-date figures, see www.irrationalexuberance.com. 16 Quoted in the Wall Street Journal, 25 February 1993. 17 ‘Farewell to Cheap Capital? 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. RIDING THE GRAVY TRAIN 1 J. K. Galbraith, Money: Whence It Came, Where It Went, 2nd edn, London, 1995. 2 Lawrence Mishel, ‘CEO-to-Worker Pay Imbalance Grows’, Economic Policy Institute, June 2006. 3 Ian Dew-Becker and Robert Gordon, ‘Where Did the Productivity Growth Go?

Principles of Corporate Finance by Richard A. Brealey, Stewart C. Myers, Franklin Allen

Then use the corresponding interest rate. 30All the examples in this section are forward-looking; they call for the value today of a stream of future debt-equivalent cash flows. But similar issues arise in legal and contractual disputes when a past cash flow has to be brought forward in time to a present value today. Suppose it’s determined that company A should have paid B \$1 million 10 years ago. B clearly deserves more than \$1 million today, because it has lost the time value of money. The time value of money should be expressed as an after-tax borrowing or lending rate, or if no risk enters, as the after-tax risk-free rate. The time value of money is not equal to B’s overall cost of capital. Allowing B to “earn” its overall cost of capital on the payment allows it to earn a risk premium without bearing risk. For a broader discussion of these issues, see F. Fisher and C. Romaine, “Janis Joplin’s Yearbook and the Theory of Damages,” Journal of Accounting, Auditing & Finance 5 (Winter/Spring 1990), pp. 145–157.

NPV, properly interpreted, wins out in the end. 5-1 A Review of the Basics Vegetron’s chief financial officer (CFO) is wondering how to analyze a proposed \$1 million investment in a new venture called project X. He asks what you think. Your response should be as follows: “First, forecast the cash flows generated by project X over its economic life. Second, determine the appropriate opportunity cost of capital (r). This should reflect both the time value of money and the risk involved in project X. Third, use this opportunity cost of capital to discount the project’s future cash flows. The sum of the discounted cash flows is called present value (PV). Fourth, calculate net present value (NPV) by subtracting the \$1 million investment from PV. If we call the cash flows C0, C1, and so on, then We should invest in project X if its NPV is greater than zero.”

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

Set up direct deposit with your company to put a percentage of your salary into an investment account every time you're paid. 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!

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The Doomsday Calculation: How an Equation That Predicts the Future Is Transforming Everything We Know About Life and the Universe by William Poundstone

In The Theory of Investment Value (1938), Williams maintained that the value of any asset resides in its future income stream, discounted to present value. This is known as the discounted cash flow model. According to Williams, a dividend-paying stock is worth the sum of all its future dividend payments, suitably adjusted. Suppose Coca-Cola pays a dividend of \$1.59 a share and will pay that same yearly dividend for the next hundred years. The total would be \$159. These dividends must be adjusted to reflect the time value of money. A \$1.59 dividend now is worth more than a \$1.59 dividend to be paid a hundred years from now. The difference is expressed in a discount rate that factors in inflation, risk, and opportunity costs. You would find that the value of a share of Coca-Cola ought to be a good deal less than \$159. What if a stock doesn’t pay dividends? There are two answers. Either the investor intends to hold the stock a long time and expects it to pay dividends in the future; or (more likely) she expects to sell the stock at a profit.

With discounted cash flow, here’s what the stock ought to be worth to you right now: • \$9.47 if the stock survives another ten years before going bust • \$18.03 if it survives another twenty years • \$39.10 if it survives fifty years • \$62.76 if it survives one hundred years • \$100 if it survives forever In Reynolds’s example the dividend grows almost fast enough to make up for the time value of money. So a stock that pays ten years of dividends before fizzling out is worth just a little shy of \$10. With longer corporate lifespans, the current value becomes progressively less than the sum of the future dividends. A hundred years of future dividends has a present value of \$62.76, rather than \$100. It would take an infinite future of dividends to be worth \$100 to an investor right now. No one can predict the next quarter, much less dividend payouts of coming decades.

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Home Building Secrets: Save Thousands Building Your Next Home: For the first time homeowner or the second time homeower who did not learn from their first mistakes by Ronald Jones

Your local electric utility tells you that the 14.0 SEER unit will cost you about \$800.00 a year to operate. So, the higher efficiency unit should cost 23% less or about \$616.00 a year; a savings of \$184.00 a year. Both units should last 15 years, so the total saving associated with the 18.0 SEER unit is \$2760.00, which is less than the \$2500.00 initial price difference. Certainly, you should consider the time value of money (what you did not earn by keeping the \$2500.00 in your pocket), and you must consider the rising cost of energy of the next 15 years. I would say that if you escalated the price of electricity (or gas) 2-3% a year, you will find that the 18.0 SEER unit produces significant savings in comparison to the 14.0 SEER unit. You will pay more now, but start saving the day you move in. Try to install standard size return-air-grilles that house your air filters.

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The Big Secret for the Small Investor: A New Route to Long-Term Investment Success by Joel Greenblatt

If our estimate of value can change dramatically with even small changes in our guesses about the proper earnings growth rate to use or the proper discount rate, how meaningful can the estimates of value made by “experts” really be? The answer to #4 above is—“not very.” As it turns out, there actually are 24-hour locksmiths in the Bronx—unfortunately, they are not available now. 1. These concepts involve a discussion of the time value of money and discounted cash flow. If you are already very familiar with these (and can’t possibly see how I can make them funny), feel free to look at the pretty pictures and then skip ahead to the chapter summary! 2. In reality, we should look for how much cash we receive from the business over its lifetime. For our purposes, we will assume that earnings are a good approximation for cash received.

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

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. Although in the practice, the minimum period for an interest period is a day. 4.

BHATTI, The Theory and Empirics of Exchange Rates, World Scientific Publishing Company, 2009, 512 p. Salih N. 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. Riccardo REBONATO, Volatility and Correlation, in the Pricing of Equity, FX and Interest-Rate Options, John Wiley & Sons, Ltd, Chichester, 1999, 360 p.

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Value Investing: From Graham to Buffett and Beyond by Bruce C. N. Greenwald, Judd Kahn, Paul D. Sonkin, Michael van Biema

The Present Value of Current and Future Cash Flows There is wide agreement in theory that the intrinsic value of any investment asset-whether an office building, a gold mine, a company selling groceries at the comer or groceries over the Internet, a government bond, or a share of General Motors stock-is determined by the present value of the distributable cash flows that the asset supplies to its owner. Present value is properly calculated as the sum of present and future cash flows, both outlays and receipts, with each dollar of future cash flow appropriately discounted to take into account the time value of money (see Appendix to this chapter). Graham and Dodd disciples accept the concept and the calculation of present value, as do all other fundamental investors. The techniques are taught at every undergraduate and graduate school of business. Investment bankers and corporate financial officers use them. Governments depend on them to evaluate the returns from potential capital projects and other investments.

At 8 percent interest, compounded annually, in two years a dollar deposited today will be worth \$1.00x(1+.08)x(1+.08), or \$1.164. Conversely, a dollar guaranteed to us two years in the future, at a discount rate of 8 percent, has a present value of \$1.00 x 1/(1.08) x 1/(1.08), or \$.857. The present value of the future cash flow is reduced more the longer we have to wait for it. The expression that captures this relationship is the time value of money. Combined with the right algebra, the concept allows us to transform a whole series of future values into their value today. The two variables we need are time, which is almost always stated in years, and the other expression that we have called both interest and the discount rate. Both terms refer to the rate at which people will voluntarily commit funds to acquire the asset in question.

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Money Moments: Simple Steps to Financial Well-Being by Jason Butler

A few years later, when I decided to train to become a professional financial planner and investment manager, I realised that I needed to raise my mathematics skills to a much higher level. I enrolled on a suitable weekly advanced mathematics night class. The tutor was fun and highly engaging and stated that we were all perfectly capable of learning advanced maths, if we had a positive attitude, put in the work, and didn’t give up. I learned about the time-value of money, geometric mean, standard deviation, dispersion and a range of other advanced financial principles. With the tutor’s encouragement and enthusiasm I progressed rapidly and also became adept at using spreadsheets and a financial calculator. Eventually I passed both my investment management and financial planning examinations and over the next twenty years built a highly successful career in financial planning.

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

This means that there is a 70% chance the option will be worth nada, a 20% chance it will be worth \$10 (if the share price in one year is \$120) and a 10% chance it will be worth \$20 (if the share price in one year is \$130). 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.

If IBM had sold the shares in the market then any gain would have been recognized straight away – IBM would have to pay tax on the gain. 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. Many entrepreneurs had taken advantage of the manic demand for Internet stock to go public.

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

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The Dhandho Investor: The Low-Risk Value Method to High Returns by Mohnish Pabrai

One year is a very good holding time frame, but if you understand the business well before buying it, I believe a longer time frame is fully warranted and justified. The Magic Formula suggests that you buy stocks that you know nothing about and hold for 12 months. It makes logical sense that you’d want to allow a longer holding period on businesses you actually understand well. If you have a very high degree of conviction on underlying intrinsic value, feel free to hold on to losers for longer than two to three years, but always be cognizant of the time value of money. It is very hard to make up the lost non-compounding years. The two-to-three-year rule prevents us from running when the lion roars—it helps avoid distressed sales at points of maximum pessimism. A wonderful example of a loudly roaring lion is my roller-coaster ride with Universal Stainless & Alloy Products over the past four years. UNIVERSAL STAINLESS & ALLOY PRODUCTS Universal Stainless & Alloy Products, Inc.

Investment: A History by Norton Reamer, Jesse Downing

Rather, religious views, sometimes not aligned with the optimal course of action ﬁnancially, were close to the surface of all economic activities undertaken in ancient civilizations. 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.

However, this remarkable history of disapproval, restriction, condemnation, and punishment for charging interest, which in some cases focused on prevailing conceptions of excessive interest rates and in other cases involved rejection of all interest charges at any level, seems to ignore a basic fact of economic life: interest rates can properly reﬂect creditor risk and time value. 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. We know from experience that widely divergent interest rates in different time periods, for different debt maturities, levels of credit exposure, and rates of inﬂation can all be fair.

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Numpy Beginner's Guide - Third Edition by Ivan Idris

We extracted the even elements from an array using a Boolean conditon with the NumPy extract() functon (see extracted.py ): from __future__ import print_function import numpy as np a = np.arange(7) condition = (a % 2) == 0 print("Even numbers", np.extract(condition, a)) print("Non zero", np.nonzero(a)) Financial functions NumPy has a number of fnancial functons:  The fv() functon calculates the so-called future value . The future value gives the value of a fnancial instrument at a future date, based on certain assumptons.  The pv() functon computes the present value (see https://www.khanacademy. org/economics-finance-domain/core-finance/interest-tutorial/ present-value/v/time-value-of-money ). The present value is the value of an asset today.  The npv() functon returns the net present value . The net present value is defned as the sum of all the present value cash fows.  The pmt() functon computes the payment against loan principal plus interest.  The irr() functon calculates the internal rate of return . The internal rate of return is the efectve interested rate, which does not take into account infaton.  The mirr() functon calculates the modifed internal rate of return .

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

The Three-Factor Model The alternative hypothesis, as we’ve already mentioned, is that there is no excess return without increased risk exposure. 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. Everyone earns the risk-free rate. So in the Fama-French universe, the only important decision you have to make is how much exposure you want to the other three factors.

Bulletproof Problem Solving by Charles Conn, Robert McLean

There is also uncertainty about future feed‐in tariffs that have been set to encourage sales of solar PV. This has to be considered against rising retail prices for electricity customers. At \$1,500 per year, the cost savings lost by waiting would be \$4,500 over three years, so the up‐front cost of the solar PV installation would have to fall by 75% to make waiting worthwhile. Rob could have used a net present value analysis where the time value of money is considered rather than a simple payback. But in this case the simple method is fine: He felt comfortable with the four‐year payback providing an implied rate of return of 25%. It was worth doing now. Finally, he wanted to estimate how much of his CO2 footprint he would reduce by going ahead. This depends on two things—one is what fuel source he is displacing (coal or gas in this case), and the second is the kilowatt hours (kWh) he is generating compared to his electricity use, which he knew from the first step.

Raw Data Is an Oxymoron by Lisa Gitelman

These lines are the supply and demand curves, whose intersection enables economists to represent how markets determine price, according to the theory of equilibrium. 12. “What Is Capital?” 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.

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

THE CHAIRMAN'S SECRET RECIPE One of the bedrocks of modern corporate finance theory is that the value of any security is the present value of its future cash flows. 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.

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The Money Machine: How the City Works by Philip Coggan

This attracted some criticism that its rules were too lax but it did allow the market to steal a march on its US rivals. HOW INVESTORS VALUE COMPANIES Why do share prices move up and down? What makes some companies into poor investments and others into the equivalent of pools winners? In the end, the price of a share should be equal to the value of all future cashflows that the investors will receive, discounted to allow for the time value of money. But it is very difficult to agree on the right discount rate and even more difficult to estimate all the future cashflows. So investors have to find some short cuts. One obvious step is to look at profits. But what is profit? It is not quite as simple as deducting a company’s costs from its revenues. A charge must also be made for the gradual fall in the value of a company’s fixed assets.

A Primer for the Mathematics of Financial Engineering by Dan Stefanica

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.

When Free Markets Fail: Saving the Market When It Can't Save Itself (Wiley Corporate F&A) by Scott McCleskey

Not all factors are quantifiable, some are quantifiable but not monetizable (time is often difficult to monetize unless it is in the context of an hourly fee), and some are both quantifiable and monetizable. Because regulations are meant to be in effect into the future rather than simply at a point in time, a calculation is normally performed to express the costs and benefits in current dollars, in order to recognize the time value of money. Once costs and benefits are estimated, they may be expressed as a specific number (which is nonetheless understood to be an estimate) or as a range. If the estimate is expressed in both a quantified range and a monetized range, the monetized range may not be a straightforward multiplication of the quantified range by a fixed cost, but will generally reflect the fact that the per-unit cost is also subject to variation.

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

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.” When many of the projects – particularly today because of technology – have a positive ROI even in down economic times, they’re not funded because it takes you a number of years because of the depreciation schedule on that investment to get your money back.

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Smarter Investing by Tim Hale

However, if you placed a deposit for two years (leaving aside the credit risk issue above) you would expect to receive a higher rate of interest for tying up your money. That is because (a) your money can erode in spending power terms through the effects of inflation; (b) you have an opportunity cost of tying up your money which the borrower needs to compensate you for; (c) you have the risk of not knowing what return you will be able to reinvest the interest payments at. This is known as the time value of money. The flip side of the increased expected return from owning a bond that matures further into the future is that its price, which moves to reflect the market’s ever-changing yield requirement, will be more sensitive to movements in yields. The bond see-saw above explains the generic relationship between yields and prices but it only tells us that as yields rise, bond prices fall and vice versa.

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

Decades later, Fisher’s ‘Debt Deflation Theory of Great Depressions’ was rediscovered by the non-orthodox economist Hyman Minsky, while at much the same time Fisher’s pre-Great Depression theory was formalized into the efficient markets hypothesis. 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. F. Sharpe. Risk and return It seems reasonable, a priori, to argue that an asset that gives a high return is likely to be riskier than one that gives a lower return.

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Capitalism: Money, Morals and Markets by John Plender

In part, it was because extending credit was seen as an act of friendship and trust, so there was a moral and social dimension to the activity. 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. The moral basis of trade thus appeared dubious, while usury, or making money out of money, was still worse.

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Lying for Money: How Fraud Makes the World Go Round by Daniel Davies

Fences for long firm fraudsters always have the cast-iron excuse that the business did not look like a fraud when they were dealing with it, because it did not, and in general, they have to screw things up pretty badly to end up being convicted. The time dimension doesn’t make it easy for everyone involved in a fraud, however. Although it puts distance between the crime and its discovery, that distance comes at a cost. Business people expect to be paid for waiting – that’s why they say things like ‘time is money’. And the time value of money means that while a sum of undiscovered fraud exists, the size of the deception is often growing. This complicates the economics of the thing a lot. 3 THE SNOWBALL EFFECT ‘Accumulate! Accumulate! That is Moses and the Prophets!’ Karl Marx, Grundrisse Ponzi and his scheme The signs, it is almost trite to observe, were there. Charles Ponzi arrived as an almost penniless Italian immigrant to Boston in 1903, having lost all his money to a card shark en voyage and owning only a ticket via New York to meet his relatives in Pittsburgh.

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

Now gold would start to flow back to the nation that had originally lost it. 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. Most international trade was financed by short-term trade bills and letters of credit that were self-liquidating when the imported goods were received by the buyer and resold for cash without any gold transfers.

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Early Retirement Extreme by Jacob Lund Fisker

In fact, outsourcing is a financial decision that should not be made blindly. 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. understand the difference between assets and liabilities. Understand leverage and cash flows. In particular, learn what is an investment (an income generating asset) and what is not an investment (items for personal use).

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

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. SPI countered with a proposal that asked the Port Authority to backstop all three towers—two of them upfront and the third once these buildings were financially stabilized.

The PA thought it almost had a deal, but Silverstein started talking about all the things on the arrangements for Tower 4 that bothered him. 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.

As Eliot Brown wrote, “the agency has taken the position that a tenant’s rent is private information, and should be withheld given that it could impair the agency.” (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.

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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

Barclays settled with BPI after a one-day public hearing in February 2010. 3. 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. After de Moivre’s death, the refinement of mortality calculations was continued in London by Richard Price, friend of Thomas Bayes and Benjamin Franklin, and founding actuary of the Equitable Life Assurance Society. 8.

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The Startup Way: Making Entrepreneurship a Fundamental Discipline of Every Enterprise by Eric Ries

Alexis Ohanian, Without Their Permission: The Story of Reddit and a Blueprint for How to Change the World (New York: Grand Central, 2016), p. 5. 6. quora.com/​Amazon-company-What-is-Amazons-approach-to-product-development-and-product-management. 7. Jack Stack and Bo Burlingham, A Stake in the Outcome: Building a Culture of Ownership for the Long-Term Success of Your Business (New York: Doubleday Business, 2002). 8. With apologies to our friends in finance, who would say that this simplistic formula is not quite right: 1. We’re not taking into account the time value of money; the payoff is only \$1 billion in future dollars, we need a net-present-value (NPV) calculation, and 2. This is actually more like an option, which should be valued according to the Black-Scholes formula, or something similar. Granted! But these involve complexity that few practitioners understand. Some of these advanced issues are discussed in Chapter 9. 9. This is why we call it a minimum viable product.

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

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.

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

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. He executed this business by buying up convertible bonds, “stripping” the option embedded in the bonds, and selling it to the equity desk to then pass along to clients who wanted long-term options on individual stocks.

The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, Moorad Choudhry

The simple margin is calculated as follows 100 100 ( 100 – 99.99 ) Spread for life = ---------------------------------------------- + 45 --------------- = 46.0481 basis points 99.99 0.9583 At the bottom of the YA screen in Exhibit 7.1 is a box labeled “MARGINS.” The Enron ﬂoater’s spread for life is 46.06. The slight difference between our calculation and Bloomberg’s is likely due to rounding error. Note also that spread for life considers only the accretion/amortization of the discount/premium over the ﬂoater’s remaining term to maturity and considers neither the level of the coupon rate nor the time value of money. Adjusted Simple Margin The adjusted simple margin (also called effective margin) is an adjustment to spread for life. This adjustment accounts for a one-time cost of carry effect when a ﬂoater is purchased with borrowed funds. Suppose an investor has purchased \$10 million of a particular ﬂoater. A leveraged investor has a number of alternative ways to ﬁnance the position, the most common being via a repurchase agreement.

Financial Statement Analysis: A Practitioner's Guide by Martin S. Fridson, Fernando Alvarez

According to one analyst, Wal-Mart's 8 percent stock price decline represented “somewhat of an overreaction.” In reality, the price drop was an overreaction in its entirety. Changing the accounting method altered neither the amount of cash ultimately received by the retailer nor the timing of its receipt. The planned change in Wal-Mart's revenue recognition process therefore entailed no loss in time value of money. Lest anyone mistakenly continue to attribute economic significance to the timing of the revenue recognition, Wal-Mart explained that the small reduction in reported earnings in the third fiscal quarter would be made up in the fourth. On top of everything else, management had already announced the accounting change prior to its August 9 conference call. An institutional portfolio manager spoke truly when he called the market's reaction to the supposed news “more confusion than anything else.”

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Financial Freedom: A Proven Path to All the Money You Will Ever Need by Grant Sabatier

For example, if your child is three years old today, you won’t need that \$80,000 college tuition money for the next fifteen years, so you need to calculate how much you need to save today at 7 percent expected annual compounding rate so it will be worth \$80,000 in fifteen years. Using a really simple calculation (and one of the most valuable in personal finance) known as the present value formula, which measures the time value of money, you can measure how much you need to invest today to get the \$80,000 over the next fifteen years: PV (present value) = amount of money you need to invest to get to your goal FV (future value) = how much money you need for college tuition (e.g., \$80,000) r = investment growth rate adjusted for inflation (e.g., 7 percent expressed as 1.07) n = number of years for the money to grow (e.g., 15 years) So for this example, PV = \$80,000(1/(1.07)^15) = \$28,995.68.

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The Code of Capital: How the Law Creates Wealth and Inequality by Katharina Pistor

Bills were also a convenient vehicle for getting around anti-usury rules, which prohibited or at least capped interest rates. Sellers who accepted a bill in lieu of payment typically required an amount exceeding the price of the good, and merchant banks discounted them as well. This may look like an interest rate, but it withstood usury policing, because it was deemed a risk premium rather than a charge for the time value of money. Charging money for time, which was of God’s making according to church doctrine, was prohibited as immoral.27 Not every regulatory arbitrage around usury rules, however, passed muster in the courts, both canon and secular, that policed them. Transactions that flipped bills between two parties without exchanging goods, merely to make profits of exchange rate differentials, for example, were condemned as “dry exchanges” and struck down.28 These and similar restrictions have since fallen by the wayside and turned carry trades from outlawed transactions into hugely lucrative deals.29 The emergence and widespread use of bills of exchange are often cited as evidence of the law merchant—a set of purely private practices that sustained long-distance trade without relying on the state, its laws, or its coercive powers.

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

The fiscal and political reality on the ground implied that this was the central case forecast. 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: 469 words: 132,438

Taming the Sun: Innovations to Harness Solar Energy and Power the Planet by Varun Sivaram

A better way to assess the economics of solar power is to compare the cost of the electric energy, rather than power, that it produces with the cost of the same amount of energy from other sources. Electric energy is measured by the kilowatt-hour (kWh), a kilowatt of power output sustained for one hour [1,000 kWh amount to a megawatt-hour (MWh)]. Calculating this cost entails spreading out the up-front cost of a solar installation over the energy that it produces over its lifetime, taking into account the time value of money. The investment bank Lazard calculated that the cost of utility-scale solar was in some cases lower than \$50 per MWh in 2016, comparable with the cost of electricity from the cheapest fossil fuel (natural gas).60 Still, as chapter 3 explains, even a low cost per kilowatt-hour can fall short of making solar competitive if the cost of solar exceeds the value that it provides. Throughout all the upheaval, bankruptcies, and price swings of recent decades, the solar industry and market has grown consistently and rapidly.

Adam Smith: Father of Economics by Jesse Norman

This includes, for example, some of the long-term economic effects of climate change or population growth and decline, which fall outside the normal time horizons of most if not all public and private investors. But this fact creates a problem. Normally future income and expenditure are discounted relative to the present, to reflect the human preference for the near over the longer term. This is the so-called time value of money, and it is one of the basic foundations of economic analysis. But at any normal discount rate the effect of discounting over such long periods is to reduce the present value of such further future payments to close to zero. Yet long-term projects such as dams and other infrastructure can obviously have continuing value, and their operating lives may run for a century or more; even today much of London’s sewage system is based on pipes, wells and drains constructed in the Victorian era.

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

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. Specifically, the current value is the expected discounted value of the dividend and value next period: Hence, to value a stock, we must be able to estimate the expected dividend payment next time period.

Mastering Private Equity by Zeisberger, Claudia,Prahl, Michael,White, Bowen, Michael Prahl, Bowen White

The sense of urgency in PE investments results from the ambitious return expectations that need to be realized over a defined investment horizon. PE firms can achieve their desired returns only if they act as transformation agents during their relatively short period of ownership. The standard return measure in PE, the internal rate of return (IRR), contributes to this urgency by including both the time value of money and the length of the holding period in its calculation. While there is no single ingredient or “secret sauce” that enables the success of PE investors, it is the focus and urgency across a number of dimensions that make its ownership culture different in aggregate, leading to a high-pressure environment but also a shared sense of direction. STRATEGIC ALIGNMENT: PE investors, management teams and independent advisors work to reposition the business, reformulate strategy and closely monitor its progress post-investment.

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

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. From the point of view of the citizen, TGC must fulfill four criteria: Reducing Corruption: Transaction Governance Capacity 85 1.

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

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? The classical gold standard holds considerable appeal because it produced an extraordinary interlude of per capita income growth and price stability in the 19th century.

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Derivatives Markets by David Goldenberg

What would be the value of that position at time T? g. Now think of the economics of e. and f. 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′)? 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? 3. (Calculating Equilibrium Forward Prices) At 12:27 p.m. on March 26, 2014 Google stock was trading at \$1,155.32.

pages: 1,073 words: 302,361

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

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. According to Birmingham, the commercial paper of these small businesses in lower Manhattan would be discounted at between 8 to 9 percent.

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

What more could boards of directors and shareholders do to ensure that managers pursue long-term value creation? 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. Keep in mind one important caveat: a company will create value only if its ROIC is greater than its cost of capital (the opportunity cost for its investors).