Business
The Time Value Of Money
The time value of money is a fundamental concept in finance that recognizes the potential for money to grow in value over time. It acknowledges that a dollar received today is worth more than a dollar received in the future due to its potential for earning interest or investment returns. This principle is crucial for making informed financial decisions and evaluating investment opportunities.
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9 Key excerpts on "The Time Value Of Money"
eBook - PDF- Hussein K. Abdel-Aal, Mohammed A. Alsahlawi(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
69 4 Time Value of Money (TVM) in Capital Expenditures M. Bassyouni This chapter is devoted to an examination of some basic relationships that relate interest to a given capital of money (either expenditure or income) over a given period of time. It is essential to consider the effect time has on capital, as capital must always produce some yield. Time value of money (TVM) is the value of money figuring at a given amount of interest earned over a given amount of time. TVM is the central concept in finance theory . CONTENTS 4.1 Basic Definitions .......................................................................................... 70 4.1.1 Capital Investment ........................................................................... 70 4.1.2 Interest ............................................................................................... 70 4.2 Types of Interest ........................................................................................... 71 4.3 Interest Calculation ...................................................................................... 71 4.4 Effective Interest .......................................................................................... 73 4.5 Annuities and Periodic Payments ............................................................. 76 4.5.1 Derivation of the Basic Equation (Sinking Fund Factor) ............ 77 4.5.2 Applications of the Annuity Technique ....................................... 78 4.5.2.1 Determining the Annual Depreciation Costs ............... 78 4.5.2.2 Determining the Annual Capital Recovery Costs ....... 78 4.6 Capitalized Costs ......................................................................................... 81 4.6.1 Calculation of Capitalized Costs of an Asset to Be Replaced Perpetually .......................................................................
eBook - PDF- Donald E. Kieso, Jerry J. Weygandt, Terry D. Warfield(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
In accounting (and finance), the phrase time value of money indicates that a dollar received today is worth more than a dollar promised at some time in the future. Why? Because of the opportunity to invest today’s dollar and receive interest on the investment. Yet, when decid- ing among investment or borrowing alternatives, it is essential to compare today’s dollar and tomorrow’s dollar on the same footing—to compare “apples to apples.” Investors do that by using the concept of present value, which has many applications in accounting. The Importance of Time Value Concepts Financial reporting uses different measurements in different situations—historical cost for equipment, net realizable value for inventories, fair value for investments. As we discussed in Chapters 1 and 3, the FASB increasingly is requiring the use of fair values in the measurement of assets and liabilities. However, for many assets and liabilities, market-based fair value information is not available. In these cases, fair value can be estimated based on the expected future cash flows related to the asset or liability. Such fair value estimates are generally considered Level 3 (most subjective) in the fair value hierarchy. They are based on unobservable inputs, such as a company’s own data or assumptions related to the expected future cash flows associated with the asset or liability. As discussed in the fair value guidance, present value techniques are used to convert expected cash flows into present values, which represent an estimate of fair value. [1] (See the FASB Codi- fication References near the end of the chapter.) Some of the applications of present value-based measurements in accounting topics, which we discuss in this text, include the following. 1 1 GAAP addresses present value as a measurements basis for a broad array of transactions, such as accounts and loans receivable [2], leases [3], postretirement benefits [4], asset impairments [5], and stock-based com- pensation [6].
eBook - PDFEntrepreneurial Finance for MSMEs
A Managerial Approach for Developing Markets
- Joshua Yindenaba Abor(Author)
- 2016(Publication Date)
- Palgrave Macmillan(Publisher)
Part IV Valuation 259 © The Author(s) 2017 J.Y. Abor, Entrepreneurial Finance for MSMEs, DOI 10.1007/978-3-319-34021-0_11 11 Time Value of Money Learning Objectives By the end of this chapter, you should be able to: • appreciate the concept of ‘time value of money’ • compare simple and compound interest • calculate future value lump sum and prevent value lump sum • distinguish between effective rate and stated rate • explain and calculate perpetuities • calculate future and present values based on annuities • distinguish between ordinary annuity and annuity due • explain and calculate amortisation 11.1 Introduction The concept of time value of money deals with the fact that ‘a dollar today is worth more than a dollar tomorrow’. This means it will take more future dollars than current dollars to buy the same quantity of goods and services because of the effect of inflation. If you have the opportunity to receive US$2,000 today or US$2,000 in a year from today, which would you prefer? Naturally, you would take the US$2,000 today because you recognise The Time Value Of Money. Receiving the US$2,000 today gives you the opportunity to invest the money in order to earn interest. In a year’s time you are likely to receive an amount bigger than the US$2,000. Assuming the US$2,000 can be put in fixed deposit with interest rate of 16 % per annum. Then, the value of the investment after one year will be worth US$2,000 plus US$320 or US$2,320. We got the interest amount of US$320 by multiplying the interest rate of 16 % by the principal of US$2,000. The dollar of US$2,000 today is obviously worth more than the US$2,000 in future. For you to be convinced to part with your money for some time, you would need to be convinced of a rate of interest. In a world where there is certainty in all cash flows, the rate of interest can be used to express the time of money. With the rate of interest, it is possible to adjust the cash flows to any particular point in time.
eBook - PDF- Robert Parrino, David S. Kidwell, Thomas Bates, Stuart L. Gillan(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The idea that money has a time value is one of the most fundamen- tal concepts in the field of finance. The concept is based on the idea that most people prefer to consume goods today rather than wait to have similar goods in the future. Since money buys goods, they would rather have money today than in the future. Thus, a dollar today is worth more than a dollar received in the future. Another way of view- ing The Time Value Of Money is that your money is worth more today than at some point in the future because, if you had the money now, you could invest it and earn interest. Thus, The Time Value Of Money is the opportunity cost of forgoing consumption today. Applications of The Time Value Of Money focus on the trade-off between current dollars and dollars received at some future date. This is an important element in financial decisions because most investment decisions require the comparison of cash invested today Concluding Comments This chapter has introduced the concept of time value of money and the basic principles of present value and future value. The table at the end of the chapter summarizes the key equa- tions developed in the chapter. The equations for future value (Equation 5.1) and present value (Equation 5.4) are two of the most fundamental relations in finance and will be applied throughout the rest of this textbook. Before You Go On 1. What is the difference between the interest rate (i) and the growth rate (g) in the future value equation? APPLICATION 5.6 Calculating Projected Earnings Problem Disney’s net income in 2019 was $11.05 billion. Wall Street analysts expect Disney’s earn- ings to increase by 1.55 percent per year over the next three years. Using your financial calculator, determine what Disney’s earnings should be in three years. Approach This problem involves the growth rate (g) of Disney’s earnings. We already know the value of g, which is 1.55 percent, and we need to find the future value.
- David Whitman, Ronald Terry(Authors)
- 2022(Publication Date)
- Springer(Publisher)
3 C H A P T E R 2 Interest and The Time Value Of Money 2.1 TIME VALUE OF MONEY When an individual or a company desires to invest an amount of capital in a long-term project, the effect of time on the value of that capital needs to be considered. The effect of time on the value of money can be illustrated by the following examples. Consider a sum of $1000 that an individual has accumulated. If the $1000 were buried in a can under a tree for some future need, the individual, one year later, would still have $1000. However, if the $1000 were placed in an insured savings account earning 3% interest for one year, the amount would have grown to $1030. Obviously, the length of time and the different investment opportunities (represented by different interest rates) lead to varying amounts of money that the $1000 can yield at some future date. A second example deals with the same $1000 and its purchasing power as a function of time. Suppose an individual has a choice of purchasing 1000 items now at a price of $1.00 per item or waiting until a future date to make the purchase. If, over the course of one year, the price increased to $1.03 per item, the $1000 will only be able to purchase 970 items. Thus, the value, in terms of purchasing power, has decreased with time. The longer the life of the project, the more important will be the considerations of The Time Value Of Money. Other factors that affect the outcome of investment projects are inflation, taxes, and risk. These will be discussed later in the text. 2.2 SOURCES OF CAPITAL There are, in general, two sources of capital needed to make an investment. Capital can be obtained either from the investor’s own funds or from a lender. Wherever capital is obtained, there is a cost associated with the use of the funds. If they are obtained from a lender, the cost of capital is the interest rate at which the funds are loaned to the investor.
eBook - PDF- Donald E. Kieso, Jerry J. Weygandt, Terry D. Warfield(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
After studying this chapter, you should have a better understanding of time value of money principles and discounted cash flow techniques as they are applied in accounting measurements. Sources: Ernst and Young, “Valuation Resource Group: Highlights of November 2010 Meeting,” Hot Topic—Update on Major Accounting and Auditing Activities, No. 2010-59 (5 November 2010); http://www.fasb.org/project/valuation_ resource_group.shtml#background (March 24, 2011); and Accounting Standards Update 2017-04, Intangibles— Goodwill and Other (Topic 350): Simplifying the Test for Goodwill Impairment (January 2017). Review and Practice Go to the Review and Practice section at the end of the chapter for a targeted summary re- view and practice problem with solution. Multiple-choice questions with annotated solutions as well as additional exercises and practice problem with solutions are also available online. Basic Time Value Concepts 6-3 LEARNING OBJECTIVE 1 Describe the fundamental concepts related to The Time Value Of Money. In accounting (and finance), the phrase time value of money indicates a relationship be- tween time and money—that a dollar received today is worth more than a dollar promised at some time in the future. Why? Because of the opportunity to invest today’s dollar and receive interest on the investment. Yet, when deciding among investment or borrowing alternatives, it is essential to be able to compare today’s dollar and tomorrow’s dollar on the same footing—to compare “apples to apples.” Investors do that by using the concept of present value, which has many applications in accounting. Applications of Time Value Concepts Financial reporting uses different measurements in different situations—historical cost for equip- ment, net realizable value for inventories, fair value for investments. As we discussed in Chapters 2 and 5, the FASB increasingly is requiring the use of fair values in the measurement of assets and liabilities.
eBook - ePub- Robert Irons(Author)
- 2019(Publication Date)
- Routledge(Publisher)
2 Time Value of MoneyThe material covered in this chapter is the framework upon which the rest of the chapters in the book are built. The conception of The Time Value Of Money gets at the very heart of virtually every calculation done from this point forth. That is because the calculations used are driven by the fundamental principles, as will be seen.This chapter covers the mathematical methods (and formulas) used to calculate the value of cash flows when either pushing them out in time (to calculate a future value) or pulling them back in time (to calculate a present value). The methods take into account the fact that corporations use other people’s money (from debtors or common stock holders) to fund their operations, and those investors deserve to be paid for the use of their money.The Cost of Money
Like everything else in life, money has a cost; that is, raising money costs money. Corporations raise money in two general forms: debt (borrowing money) and equity (selling partial ownership in the firm). The cost of debt is interest. To the borrower, the interest rate represents cost, while to the lender the interest rate represents income (known as its yield or return). Equity has two costs: dividends (quarterly payments of cash) and capital gains (increases in the stock’s market price). To the firm these are costs, while to the firm’s shareholders they are income. So, the total yield paid to equity holders can be broken down into the dividend yield and the capital gains yield. The cost of debt is discussed in detail in Chapter 4 , “The Term Structure of Interest Rates.” The costs of equity are discussed further in Chapter six , “Stock Valuation.”The Fundamental Principles in Action
FP1 equates the value of an asset with the present value of the cash flows the asset is expected to produce. This principle is clearly seen when calculating the present value of single or multiple cash flows, and is applied (but not so clearly) when calculating the present value of annuities. FP3 asserts the inverse relationship between the price of an asset and its yield, or return. This principle is seen when discounting is done more frequently than annually—this effectively increases the discount rate, causing the present value of the cash flows to decrease. The interaction between FP1 and FP3 is seen in PR1, which states that increasing the discount rate decreases the present value of cash flows.
eBook - PDFManagerial Accounting
Tools for Business Decision Making
- Jerry J. Weygandt, Paul D. Kimmel, Donald E. Kieso(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Would you rather receive $1,000 today or a year from now? You should prefer to receive the $1,000 today because you can invest the $1,000 and then earn interest on it. As a result, you will have more than $1,000 a year from now. What this example illustrates is the concept of The Time Value Of Money . Everyone prefers to receive money today rather than in the future because of the interest factor. APPENDIX PREVIEW Time Value of Money Appendix A 1 Compute interest and future values. • Nature of interest • Future value of a single amount • Future value of an annuity 2 Compute present values. • Present value variables • Present value of a single amount • Present value of an annuity • Time periods and discounting • Present value of a long-term note or bond 3 Compute the present value in capital budgeting situations. • Using alternative discount rates 4 Use a financial calculator to solve time value of money problems. • Present value of a single sum • Present value of an annuity • Useful financial calculator applications LEARNING OBJECTIVES 1 Compute interest and future values. LEARNING OBJECTIVE Nature of Interest Interest is payment for the use of another person’s money. It is the difference between the amount borrowed or invested (called the principal ) and the amount repaid or collected. The amount of interest to be paid or collected is usually stated as a rate over a specific period of time. The rate of interest is generally stated as an annual rate. The amount of interest involved in any financing transaction is based on three elements: 1. Principal ( p ): The original amount borrowed or invested. 2. Interest Rate ( i ): An annual percentage of the principal. 3. Time ( n ): The number of periods that the principal is borrowed or invested. A-1 A-2 Appendix A Time Value of Money COMPOUND INTEREST Compound interest is computed on principal and on any interest earned that has not been paid or withdrawn.
eBook - PDF- Laurence G. Taff(Author)
- 2002(Publication Date)
- CRC Press(Publisher)
1 1 Interest and The Time Value Of Money Mortgages in the U.S. are mostly fixed-rate securities . This chapter covers the basics of simple , compound , and continuous interest calculations and their usage in fixed -income securities with (mostly) constant cash flows. Present value , future value , and other aspects of fixed-income mathematics and definitions of key interest rate con-cepts are dealt with too. When we move on to mortgage-related derivatives, the importance of this and the next two chapters for valuation and portfolio man-agement will become even more apparent. (The first time a financially important concept is mentioned it will appear in italics.) I. BASIC INTEREST CONCEPTS A. W HAT I S I NTEREST ? “What is interest?” or, more properly put if you are a borrower, “what are interest charges ?” is an important question. Interest charges are the cost to you of renting someone else’s money. We are so used to being colloquial about it that we tend to refer only to the interest rate, or just the interest, as the cost of renting money. It should not surprise you that a cost is associated with borrowing (renting) money because a cost is associated with renting most things. Alternatively, you could be the lender. Then the question “What is interest?” means “What are the interest payments you will receive for lending out your funds?” Put differently, if you are making an investment by lending money, what will the rate of return on your venture be? You have some money. You could spend it now on goods or services. Another option is that you could lend it out to someone. Hence, a more sophisticated interpretation for the interest rate you are willing to accept is that the interest you charge is the price for your deferment of immediate consumption. With many tens of thousands of participants in the financial markets, “the” interest rate is the consensus market rate for the suspension of consumption.
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