...CHAPTER 2: THE TIME VALUE OF MONEY This chapter consists of five sections: the first section explains the time value of money and the factors that affect the time value of money; The second part will help to distinguish the types of cash flow; The next two sections will discuss how to determine the present value and the future value of cash flows; The final section will guide on how to plan an amortized loan. Before we start, we need to clarify a problem together, which is why we have to study the chapter; in other words, why financial managers must understand the time value of money? In fact, whether they are individuals or companies, most financial decisions are associated with the time value of money. Besides, the objective of financial management is to maximize shareholder value and shareholder value depends greatly on the timing of cash flow. Therefore, financial managers need to understand the time value of money to assess the flow of funds, especially in the evaluation of the ability of the investment project to generate extra value for shareholders in the future. In short, you cannot become a financial manager if you do not understand the time value of money. We will start with the question: would you like to get a million dollars today or ten years from now? The contents of this chapter will help you to get a thorough answer to this question. 1 / The time value of money and the factors that affect the time value of money: Simply put, the time value of money is the idea...
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...Introduction The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year. Additionally, the concept of time value of money is important to financial decision-making because it emphasizes earning a return on invested capital, recognizes that earning a return makes $1 worth more today than $1 received in the future and it can be applied to future cash flows in order to compare different streams of income. A dollar to be paid or received in different time periods will have different values. For instance, a dollar today is worth more than a dollar in two years from now. This is because we can invest the dollar today, which will earn us a rate of return (interest) and create an increased value in two years. This process is called compounding and it involves taking a dollar today (present value), and investing it so that it grows into a larger amount in the future (future value). Additionally, managers must also understand factors which affect time value of money such as annuities which could include interest rates, opportunity costs, future and present values of money, and compounding. According to Brealey, Myers & Marcus, 2004, “each time value of money has five variables: interest rate or return, time or number of periods, future value, present value, and amount of payments either made or received” (pg. 812). The two key components of time value of money are present value (PV) and future value (FV). Present...
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...Time Value of Money: Simple Interest versus Compound Interest Outline I. Applications of Time Value of Money 1.1 Example One 1.2 Example Two 2. Interest 2.1 What is Interest? 2.2 Three Variables of Interest 1. Principal 2. Interest Rate 3. Time 2.3 Why is Interest Charged? 3. Simple Interest 3.1 What is Simple Interest? 3.2 Simple Interest Formula 4. Compound Interest 4.1 What is Compound Interest? 4.2 Compound Interest Formula 5. Compound Interest Tables 1. Future Value of $1 2. Present Value of $1 3. Present Value of an Ordinary Annuity of $1 4. Present Value of an Annuity due 5. Present Value of a Deferred Annuity 6. Conclusion 7. References Abstract The time value of money (TVM) is based on the principle that "a dollar today is worth more than a dollar in the future, (Mott, 2010, pp.31). Waiting for future dollars involves a cost -the cost is foregoing the opportunity to earn a rate of return on money while you are waiting" (pp.31). TVM was developed by Leonard Fibonnacci in 1202 and is one of the basic concepts of finance. One hundred dollars today has a different buying power than it will have in the future. For example, $100 invested in a savings account at your local bank yielding 6% annually will grow to $106 in one year. The difference between the $100 invested now-the present value of the investment-and its $106 future value represents the time value of money, (Spiceland...
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...Time Value of Money Chad McDade FIN/200 November 11, 2011 Markques McKnight Time Value of Money The time value of money tells us that money available to us today is worth more than money available to us in the future; this is because of the earning potential of money. Money has an earning potential because of interest – money placed in an interest bearing account or investment earns money. If we place $1000 in a savings account that earns 5% interest at the end of a year we would have $1050 in our account. There are four concepts to the time value of money – present value, present value of an annuity, future value, and future value of an annuity. The present value concept is the value of future payments today – as money received today is more valuable than money received in the future, money received in the future has less value today. For example, say we decide that we are presented with an investment opportunity that earns 5% interest and we want this investment to be worth $10,000 in five years – how much do we invest? Using the formula PV=FV/〖(1+i)〗^n we would be able to figure the investment amount. PV=$10,000/〖(1+.05)〗^5 PV=$7,836.99 The present value of annuity is similar to present value but is used to calculate the current value an annuity or series of payments instead of a single payment. When finding the present value of an annuity we are discounting each future payment to reflect that payment’s current value and adding...
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...Time Value of Money Terminology Terminology (AKA jargon) can be a major impediment to understanding the concepts of finance. Fortunately, the vocabulary of time value of money concepts is pretty straightforward. Here are the basic definitions that you will need to understand to get started (calculator key abbreviations are in parentheses where appropriate): Banker's Year A banker's year is 12 months, each of which contains 30 days. Therefore, there are 360 (not 365) days in a banker's year. This is a convention that goes back to the days when "calculator" and "computer" were job descriptions instead of electronic devices. Using 360 days for a year made calculations easier to do. This convention is still used today in some calculations such as the Bank Discount Rate that is used for discount (money market) securities. Compound Interest This refers to the situation where, in future periods, interest is earned not only on the original principal amount, but also on the previously earned interest. This is a very powerful concept that means money can grow at an exponential rate. Compounding Frequency This refers to how often interest is credited to the account. Once interest is credited it becomes, in effect, principal. Note that the compounding frequency and the frequency of cash flows are not always the same. In that case, the interest rate is typically adjusted to an effective rate that is of the same periodicity as the cash flows. For example, if we have quarterly cash flows...
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...MODULE 1 CASE STUDY FIN 501- THE TIME VALUE OF MONEY AND FINANCIAL STATEMENT ANALYSIS DR. JOHN HALSTEAD April 21, 2015 In this case study, I will work through a variety of time value money problems to grasp the concept of how to calculate the present and future value of a lump sum and the present and future value of an annuity. I will also learn how to calculate the present value of a perpetuity. This is important, because this enables me to learn how to determine the value of a typical corporate bond. Present Value of a lump sum, is the value of an expected income stream determined as of the date of valuation. The present value is always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money 1. a. PV=$100,000*11.0520=$94,911.41 If you were to receive $100,000.00 in 5 time periods from now, that $100,000 would be worth only $94,911.41 today. If you were to invest the $94,911.41 at a rate of .05% today then you would have $100,000 at the end of 5 time periods. So, if I had a choice between taking an amount higher than the $94,911.41 today as oppose to taking the $100,000 at the end of 5 time periods then I would take the money today. By doing so, I would be able to invest the higher amount at .05% for 5 equal time periods, which would end up being more that the 100,000. b. PV=$200,000*[1/(1.10)10]=$179,274.47 If you were to receive $200,000.00 in 10 time periods from now, that $200,000...
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... 2 Review of time value of money Simple interest Example: A firm borrows $1,000 for a year at 10% simple interest per year. How much must the firm repay after one year? FV = future value = 1,000(1+r) = 1,000 (1.1) =1,100 What if the loan is for 3 years, at compound interest of 10% per year? If compounding is annual: FV = 1,000 (1+r)3 = 1,000 (1.1)3 = 1,331 3 Review of time value of money In general, FV = PV (1+r)t = PV * FVIF (r, t) FVIF = future value interest factor On exams, if you write FV = 1,331, this is not enough. You must write at least: FV = 1,000 FVIF (10%, 3) or FV = 1,000 (1 + 0.1)3 = 1,331 If FV = PV (1 + r)t, then 1 PV FV t (1 r ) PVIF = present value interest factor 4 Review of time value of money To find r in PVIF or FVIF We know that FV = PV (1+r)t FV (1 +r)t = [(1 PV +r)t 1 t ] (1 + r ) = = FV 1 t PV FV PV 1 t 5 Review of time value of money FV r= PV 1 t -1 To solve for t, take the log: Example: PV = 25,000; FV = 50,000; r= 12%, t =? FV = PV (1+r)t 50,000 = 25,000 (1+.12)t 50,000/25,000 = 1.12t 2 = 1.12t 6 Review of time value of money Log 2 = Log 1.12t t log 1.12 = log 2 t = log2/log 1.12 = 6.1163 ‘log’ or ‘ln’ button on financial calculator 7 Review of time value of money Annuities Draw time line Eg cash flow...
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...Gregory Cayo Time value of money & inventing Davenport University/ Finc 510 Time Value of money plays a major role in our lives. Whether you are an investor or a worker, somehow you still have to deal with it. As an investor, when starting an investment with a present value, the future value would eventually make profit in the next year or so. In other words, compounding is the name given to a starting investment that generates interest. Additionally, many jobs have 401(k), which allow workers to save and invest their money after their retirement. Some companies are already stockholders. Therefore, workers can be asked to work beyond their retirement deadline when there is a crash in the market. As a result, workers might no longer benefit from their 401 (k) saving. However, they would rather be part of the government retirement plan, which offer a lot lower than the 401(k) retirement plan (Ehrhard & Brigham, 2011). Financial problems are being solved easier when using spreadsheets on excel. The use of spreadsheets provides a visual concept of time value of money including all the transactions that are made by a company. By using spreadsheets, all the calculations are being made using a specific formula respectively. It is also helpful to use a time line when solving finance problems. Whether the problem involves excel or not, a time line is usually required to set up all the formula needed. A Time line tends to simplify the amount of work in a much simpler manner...
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...Chapter One: The Marketing Landscape for Annuities Financial Services Industry The financial services industry consists of companies that offer products and services designed to help individuals, businesses, and governments meet certain financial goals, such as protecting against financial losses, accumulating and investing money or other assets, and managing debt and cash flow. Accumulation period The net amount paid for an annuity plus any interest or investment earnings, less the amount of any withdrawals or fees. Accumulation period The time period between the date that a contract owner purchases an annuity and the date that the annuity income payments begin. Annuitant The person whose lifetime is used to measure the length of time benefits are payable under an annuity contract. Annuity period The time span between each of the payments in the series of periodic annuity income payments. Annuity period The time span between each of the payments in the series of periodic annuity income payments Beneficiary The person or legal entity that receives any applicable annuity death benefit. Contract Owner The person or entity who applies for and purchase an annuity contract. Deferred Annuity An annuity under which periodic annuity income payments generally are scheduled to being at a future date, generally more than one year after the date on which the annuity was purchased. Equity-indexed annuity An annuity that offers certain principal and earnings guarantees...
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...Part 2 Valuation 3 The Time Value of Money Contents n n n Objectives After studying Chapter 3, you should be able to: n The Interest Rate Simple Interest Compound Interest Single Amounts • Annuities • Mixed Flows Understand what is meant by “the time value of money.” Understand the relationship between present and future value. Describe how the interest rate can be used to adjust the value of cash flows – both forward and backward – to a single point in time. Calculate both the future and present value of: (a) an amount invested today; (b) a stream of equal cash flows (an annuity); and (c) a stream of mixed cash flows. Distinguish between an “ordinary annuity” and an “annuity due.” Use interest factor tables and understand how they provide a shortcut to calculating present and future values. Use interest factor tables to find an unknown interest rate or growth rate when the number of time periods and future and present values are known. Build an “amortization schedule” for an installment-style loan. n n Compounding More Than Once a Year Semiannual and Other Compounding Periods • Continuous Compounding • Effective Annual Interest Rate n n n Amortizing a Loan Summary Table of Key Compound Interest Formulas Summary Questions Self-Correction Problems Problems Solutions to Self-Correction Problems Selected References n n n n n n n n n n n 39 Part 2 Valuation The chief value of money lies in the fact that one lives in a world...
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...Chapter 2 Time Value of Money MINI CASE Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination which covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (a) a $100 lump sum cash flow at the end of year 2, (b) an ordinary annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of years 0 through 3. Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A time line is a graphical representation which is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on. 0 1 2 year | | | lump sum 100 cash flow 0 1 2 3 | | | | annuity 100 100 100 0 1 2 3 | | | | uneven...
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...© Nikada/iStockphoto.com Chapter 28 Time Value of Money © Cengage Learning. All rights reserved. No distribution allowed without express authorization. In Chapter 1, we saw that the primary objective of financial management is to maximize the intrinsic value of a firm’s stock. We also saw that stock values depend on the timing of the cash flows investors expect from an investment—a dollar expected sooner is worth more than a dollar expected further in the future. Therefore, it is essential for financial managers to understand the time value of money and its impact on stock prices. In this chapter we will explain exactly how the timing of cash flows affects asset values and rates of return. The principles of time value analysis have many applications, including retirement planning, loan payment schedules, and decisions to invest (or not) in new equipment. In fact, of all the concepts used in finance, none is more important than the time value of money (TVM), also called discounted cash flow (DCF) analysis. Time value concepts are used throughout the remainder of the book, so it is vital that you understand the material in this chapter and be able to work the chapter’s problems before you move on to other topics.1 There are no Beginning-of-Chapter Questions for this chapter. 1. The problems can be worked with either a calculator or an Excel spreadsheet. Calculator manuals tend to be long and complicated, partly because they cover a number of topics that aren’t used in...
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...Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00 2. Present Value is defined as: A. Future cash flows discounted to the present at an appropriate discount rate B. Inverse of future cash flows C. Present cash flow compounded into the future D. None of the above 3. If the interest rate is 12%, what is the 2-year discount factor? A. 0.7972 B. 0.8929 C. 1.2544 D. None of the above 4. If the present value of the cash flow X is $240, and the present value cash flow Y $160, then the present value of the combined cash flow is: A. $240 B. $160 C. $80 D. $400 5. The rate of return is also called: I) discount rate; II) hurdle rate; III) opportunity cost of capital A. I only B. I and II only C. I, II, and III D. None of the given ones 6. Present value of $121,000 expected to be received one year from today at an interest rate (discount rate) of 10% per year is: A. $121,000 B. $100,000 C. $110,000 D. None of the above 7. One year discount factor at a discount rate of 25% per year is: A. 1.25 B. 1.0 C. 0.8 D. None of the above 8. The one-year discount factor at an interest rate of 100% per year is: A. 1.5 B. 0.5 C. 0.25 D. None of the above 9. Present Value of $100,000 that is, expected, to be received at the end of one year at a discount rate of 25% per year is: A. $80,000 B. $125,000 C. $100...
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...12/9/2012 Chapter 9 The Time Value of Money 1 Chapter 9- Learning Objectives Identify various types of cash flow patterns (streams) that are observed in business. Compute (a) the future values and (b) the present values of different cash flow streams, and explain the results. Compute (a) the return (interest rate) on an investment (loan) and (b) how long it takes to reach a financial goal. Explain the difference between the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR), and explain when each is more appropriate to use. Describe an amortized loan, and compute (a) amortized loan payments and (b) the balance (amount owed) on an amortized loan at a specific point during its life. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2 1 12/9/2012 Time Value of Money The principles and computations used to revalue cash payoffs at different times so they are stated in dollars of the same time period The most important concept in finance used in nearly every financial decision Business decisions Personal finance decisions Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 3 Cash Flow Patterns Lump-sum amount – a single...
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...Simple Interest and Discount Interest is the fee paid for using someone else’s money. You pay if you borrow money. You earn if you lend money. Principal – The amount of money borrowed The amount of interest paid depends on: * Interest rate * Time Time Period | Years | Stated Rate | Decimal Form | 72 days | 72/365 | 6 % | .06 | 4 months | 4/12 | Seven and one eighth % | .07125 | 18 months | 1.5 | Half a % | .005 | Interest can be computed two ways: * Simple Interest * Compound Interest Simple Interest Formula – I = Prt where: * I – the amount of interest * P – the amount of principal * r = interest rate per year * t = length of time in years Simple Interest is normally used for loans or investments of a year or less. An exception is corporate bonds. See example 1 and 2 from page 260 Future or Maturity Value for Simple Interest A = P( 1 + rt ) where A is the future or maturity value See example 3 from page 261 Do problems 4, 8, 12, 16 Present Value with simple interest – the amount deposited today (the principal) that will yield some future value. ------------------------------------------------- Since A = P(1+ rt) then : P = See examples 5 and 6 on page 263 Discount In a simple discount loan the interest is deducted in advance from the amount of the loan and the balance is given to the borrower. The full value of the loan must be paid back at maturity. Treasury bills are financial instruments...
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